EPA-650/4-75-012
June 1974
Environmental Monitoring Series
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EPA-650/4-75-012
RELATIONSHIP BETWEEN
CIRCUMSOLAR SKY BRIGHTNESS
AND ATMOSPHERIC AEROSOLS
by
Glenn F. Shaw and Charles S. Deehr
University of Alaska
Fairbanks, Alaska 99701
Grant No. 801113
ROAP No. 26AAS
Program Element No. 1AA009
EPA Project Officer: Edwin Flowers
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
WASHINGTON, D. C. 20460
June 1974
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EPA REVIEW NOTICE
This report has been reviewed by the National Environmental Research
Center - Research Triangle Park, Office of Research and Development,
EPA, and approved for publication. Approval does not signify ibit the
contents necessarily reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for use.
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S . Environ-
mental Protection Agency, have been grouped into series. These broad
categories were established to facilitate further development and applica-
tion of environmental technology. Elimination of traditional grouping was
consciously planned to foster technology transfer and maximum interface
in related fields. These series are:
1. ENVIRONMENTAL HEALTH EFFECTS RESEARCH
2. ENVIRONMENTAL PROTECTION TECHNOLOGY
3. ECOLOGICAL RESEARCH
4. ENVIRONMENTAL MONITORING
5. SOCIOECONOMIC ENVIRONMENTAL STUDIES
6. SCIENTIFIC AND TECHNICAL ASSESSMENT REPORTS
9. MISCELLANEOUS
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 quanti-
fication of environmental pollutants at the lowest conceivably significant
concentrations. It also includes studies to determine the ambient concen-
trations 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 for sale through the National
Technical Information Service, Springfield, Virginia 22161.
Publication No. EPA-650/4-75-012
11
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ABSTRACT
The color distribution and brightness gradient of diffuse skylight
within an angular distance of roughly thirty to forty degrees from the
sun depends critically on the composition, size distribution, and con-
centration of aerosols in the atmosphere. This circumsolar brightness
is added to the skylight which results from scattered sunlight in a pure
Rayleigh atmosphere. It is called the solar "aureole" and its magnitude
and spatial distribution is dependent on the physical characteristics of
aerosols in the free atmosphere. In an attempt to relate these charac-
teristics to the observation, a description of the sky radiation in a
turbid atmosphere was developed using the theory of radiative transfer
and a perturbation method which treats the aureole sky intensity as a
perturbation on an equivalent Rayleigh scattering mechanism where all
orders of scattering are considered.
In order to make accurate measurements of the diffuse sky intensity
within several degrees of the sun, it was necessary to develop a spe-
cialized instrument (sky coronameter), similar in nature to a solar
coronagraph, to reduce instrumentally-scattered light from the bright
solar disk immediately outside of the field-of-view. A well-baffled
photometer for sky radiation measurements outside 10° from the sun was
also designed and built, along with a precision direct sun photometer,
used for making complementary multi-wavelength atmospheric transmission
measurements.
Examples of sky intensity in the solar vertical plane and in the
solar almucantar (an azimuth sweep through the sun at constant elevation
angle) are presented from an arctic location near Barrow, Alaska (71°19'N,
156°37'W), a sub-arctic location at Ester Dome, Alaska (64°53'N,
m
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148°03'W), and a tropical station at Loiyengalani, Kenya (2°45'N,
36°42'E). Estimates of the aerosol scattering phase function, P(e),
were derived from the observations which include a variety of synoptic
conditions and different air-mass types. The aerosol scattering phase
functions are then compared to a library of pre-calculated phase func-
tion curves made for various assumed forms of aerosol size distribution
functions. In addition, numerical estimates were made of the columnar
aerosol mass loading, y (the total weight of aerosols contained in a
vertical column with unit cross-section) based on the best fit aerosol
size distribution and the quasi-monochromatic optical depth. Typical of
continental observations, it was found that a Junge power-law aerosol
size distribution function approximates the observed scattering phase
function rather well. More complex distribution functions cannot be
inferred legitimately from the measurements because of cumulative errors
in the process of calculating the scattering phase function from the
sky-brightness observations.
The Junge power-law exponent, v, seems to depend upon air mass
type, and to a lesser extent on local climatological conditions (ground
cover, etc.). Relatively large values of v (i.e., v=4) were found
during an episode of advected forest fire smoke from Siberia into Alaska,
Smaller values (v=2.5 to 3.0) were found during clear conditions in an
unstable, convecting atmosphere.
IV
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Table of Contents
Page
FIGURE CAPTIONS vii
TABLE CAPTIONS x
ACKNOWLEDGEMENTS xi
CONCLUSIONS xii
RECOMMENDATIONS xiv
INTRODUCTION 1
General 1
The relation between aerosols and global climate 2
The brightness or intensity of the day sky 4
THEORY OF RADIATIVE TRANSFER IN A TURBID ATMOSPHERE 9
General remarks and theory 9
Primary scattering atmosphere 12
THE EFFECT OF AEROSOLS TREATED AS A PERTURBATION ON THE
RAYLEIGH SCATTERING MECHANISM 17
First order aureole for an atmosphere containing non-
absorbing aerosols 19
INSTRUMENTATION 21
Direct sun photometer 21
Calibration of sun photometer 24
Photoelectric coronameter 28
Calibration of photoelectric coronameter 34
RESULTS AND DISCUSSION 37
Overview 37
Measurements on April 11, 1973 38
Measurements on May 1973, at Interior Alaska 38
Measurements during forest fire episode, July 1973 41
Aerosol optical depths inferred from sky intensity 50
African measurements 53
Measurements on August 20, 1973 56
Measurements on August 2, 1973 63
The effect of cirrus clouds on sky brightness 66
Measurements on September 3, 1973 68
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Page
Aerosol mass loading 68
Measurements in Arctic Alaska, March 25-31, 1974 72
Measurements on May 2, 1974 81
THE RELATION BETWEEN THE JUNGE POWER-LAW EXPONENT AND THE
AUREOLE BRIGHTNESS GRADIENT 85
REFERENCES 89
APPENDIX A 91
Units of sky brightness 91
APPENDIX B 97
Computation of geometrical parameters 97
A) The solar zenith angle 97
B) The air mass, m(z) 98
C) Scattering angle, e 99
D). Effects of altitude, h 100
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FIGURE CAPTIONS
Page
Figure la Polar plot of sky intensity for a molecular atmosphere.
Intensity is expressed in units of solar flux divided
by TT. 5
Figure Ib Sky intensity in the solar vertical plane for a molecular
atmosphere with three values of surface albedo, A. 6
Figure 2 Polar plot of sky intensity as observed at Collge, Alaska
on April 26, 1974 at 500nm. Sky radiance =irI/Fo. 7
Figure 3 Geometry relevant to solution of the radiative transfer
problem for a plane, parallel atmosphere. 10
Figure 4a Sky intensity in the solar vertical plane computed by
single-scatter approximation (dotted) and by complete
solution to the equation of transfer (solid). Sky
intensity = TT!/FO. 15
Figure 4b Same as above except computed for the solar almucantar.
Sky intensity = irl/Fo. 15
Figure 5 Photograph of the direct-sun photometer. 22
Figure 6 Schematic of electronics for direct-sun photometer. 23
Figure 7 Setup for optical calibration of sky brightness photometer. 26
Figure 8 Optical diagram of the sky-brightness photoelectric corona-
meter. 29
Figure 9 Fieldstop in photoelectric coronameter. 31
Figure 10 Optical housing of photoelectric coronameter. 33
Figure lla Sky intensity on April 11, 1973 at College, Alaska at
500nm. Normalized to 1.0 intensity unit at the zenith. 39
Figure lib Sky polarization ratio in solar vertical plane. 39
Figure 12 Sky intensity in the solar almucantar at 500nm and 700nm
normalized to 1.0 intensity unit at = 5°. 40
Figure 13a Sky intensity in the solar almucantar on July 25, 1973
at A = 500nm, College, Alaska. 42
Figure 13b Same as above, except at A = 700nm. 43
Figure 13c Sky intensity in the solar vertical plane on July 25,
1973 at A = 500nm. 44
Figure 13d Same as above, except at A = 700nm. 45
vn
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Page
Figure 14 Aerosol scattering phase function, P(e), for July 25,
1973. Curves computed for power-law distribution are
shown as light lines for different values of power-law
exponent. 49
Figure 15 Scattering phase function, P(e), computed for different
aerosol size distribution functions. 51
Figure 16a Rayleigh sky intensity, irI/Fo, in the solar almucantar
at an angular distance of 50° from the sun plotted against
optical depth T for three values of surface albedo, A. 52
Figure 16b Same as above except for four values of y . 52
Figure 17a Sky intensity, irl/Fo, in the solar vertical at Loiyen-
galani, A = 500nm. 57
Figure 17b Same as above, except A = 700nm. 58
Figure 17c Sky intensity, Til/Fo, in the solar almucantar at
Loiyengalani, A = 500nm. 59
Figure 18 Aerosol scattering phase functions deduced from sky
brightness measurements. 60
Figure 19a Sky intensity in the solar almucantar on August 20,
1973, A = 700nm. 61
Figure 19b Sky brightness in the solar vertical plane on August
20, 1973, A = 500nm. 62
Figure 20a Sky intensity in the solar vertical plane on August
2, 1973, A = 500nm. 64
Figure 20b Same as 20a, except for A = 700nm. 65
Figure 21 Temporal variation of sky intensity centered on an
evaporating jet contrail. 67
Figure 22 Sky intensity irl/Fo, on September 3, 1973, in the solar
almucantar from Ester Dome, Alaska (solid) and from
College (dashed). 69
Figure 23 Volume extinction coefficient calculated for Junge
power-law distribution for constant aerosol mass loading
of 50 yg/m3. 71
Figure 24 Aerosol optical depth versus wavelength for 3 days in
March 1974, Barrow, Alaska. 74
vm
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Page
Figure 25 Volume extinction coefficient versus wavelength
calculated for Junge size distribution function and
constant volumetric mass loading for various com-
binations of lower, r,, and upper, r2, cutoff radii. 76
Figure 26 Temporal variation of coronameter output voltage,
Barrow, Alaska. 77
Figure 27 Diurnal variation of circumsolar sky intensity at
angular distances of 1.2 and 6.2 from the sun's
limb on March 26, 1974 at Barrow, Alaska. 79
Figure 28 Sky intensity, irI/Fo, in the solar almucantar on May
2, 1974, A = 500nm, College, Alaska. 82
Figure 29 Langley plot of direct-sun data on May 2, 1974 at
College, Alaska. 83
Figure 30 Wavelength dependency of aerosol optical depth on May
2, 1974 at College, Alaska. 84
Figure 31 Ratio of sky intensity at 1.2° and 6.2 as a function
of the Junge power-law exponent, v. 87
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TABLE CAPTIONS
Table 1 Photoelectric coronameter specifications.
Table 2 Values of surface albedo measured at College, Alaska.
Table 3 Values of aerosol optical depth at Loiyengalani,
Kenya, at 500 nm and 700nm.
Table 4 Values of columnar aerosol mass loading.
Page
32
47
54
70
Table AC-1 Radiant intensities of some natural sources at
A = 550nm.
A5
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ACKNOWLEDGMENTS
We wish to thank Drs. Edwin Flowers and George Griffing for helpful
suggestions. We also appreciate the interest shown in our work by Mr.
Richard Latimer.
Dr. Donald Pack and his associates helped arrange facilities for
our use at Barrow.
Our thanks go to Mrs. Kathy Blagrove and Vicki Wade for typing the
manuscript.
Partial support was provided for this study under NSF contracts GA-
36871 and GU-40427 and by State of Alaska funds. The major support was
provided by EPA grant number R801113.
XI
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CONCLUSIONS
Measurement of the brightness gradient and absolute intensity of
scattered sky radiation in the circumsolar region within about thirty
degrees from the sun provides a practical and useful method for assessing
certain physical properties of atmospheric aerosols. For example, the
columnar mass loading and an estimation of the size distribution func-
tion for the atmospheric aerosols can be obtained from the sky-brightness
data.
The general method of analysis is most accurate, and hence most
useful for atmospheres with low turbidity. Thus, the technique is
especially useful for aerosol studies at locations far removed from
urban pollution effects. In this regard, experiments done in interior
Alaska and arctic Alaska using quasi-monochromatic sky radiation measure-
ments obtained with specialized instrumentation, demonstrate that the
aerosol size distribution and concentration sometimes fluctuates on time
scales as short as hours.
There seems to be a complex relationship between the aerosol size
distribution function and air mass type. Generally it is observed that
polar air masses have lower columnar concentrations and a relatively
larger ratio of small to large particles within the particle size spec-
trum. Forest fire smoke advected into interior Alaska from Eastern
Siberia had a size spectrum which could be approximated by a Junge
power-law distribution with an exponent value, \>, numerically equal to
4.0 +_ 0.2. Aerosols generated by local convection have been observed to
have power-law exponent equal to 2.5+0.3.
XT
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The measurements of circumsolar sky intensity yield useful esti-
mation of aerosol parameters even for extremely transparent atmospheres.
We believe that the technique has application in connection with studies
that involve the transport and origin of atmospheric aerosols.
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RECOMMENDATIONS
The aureole method of studying aerosol size distribution and mass
loading yields useful quantitative information in pure low turbidity
atmospheres. As such, the technique has the potential for monitoring
and studying aerosols at locations far from urban centers where air
purity is high. Studies of the properties of the background aerosols
are fundamentally important. For example, there has been much specu-
lation recently by scientists that the background aerosol loading may
be increasing globally due to the industrial activities of man. If
in fact this hypothesis is correct, it eventually may have an impact
on global climate because the aerosols effectively alter the radiation
budget of the earth-atmosphere system. Considerations such as these
make the problem of monitoring and quantifying the global distribution
and temporal variations of the background aerosol a fundamental one
in atmospheric science.
We strongly recommend that a network of stations be established
at existing high-altitude mountain observatories and at some high lati-
tude stations to monitor the solar aureole and establish important
baseline information on the concentration and size distribution of the
background aerosols. In view of the increasing worldwide industrial-
ization, we feel that it is imperative to implement these programs as
rapidly as possible.
xiv
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INTRODUCTION
General
The free atmosphere is charged with small participates (atmospheric
aerosols) which are of the same order of size as the wavelength of
visible light and which, as a result, interact strongly with the solar
radiation field. Because of this strong optical interaction, the color,
intensity and polarization of the day sky are modified by the presence
of these suspended particulates. Optical effects are particularly
strong at small angular distances from the sun because the aerosols
diffract relatively large amount of radiant energy in the forward, or
near forward direction, and relatively lesser amounts into the backward
or side directions. As a result, a whitish glow or aureole, which can
be attributed to the aerosols, is often observed to surround the sun.
For the reasons just stated, the circumsolar aureole is a sensitive
indicator of the presence of atmospheric particulate material, and in
fact exceedingly minute quantities of dust, such as might be found in
pure non-urban atmospheres, can cause a detectable solar aureole to
occur (Eiden, 1968; Green, Deepak, Lipofsky, 1971). Moreover, the opti-
cal characteristics of the aureole, such as the distribution of absolute
intensity as a function of scattering angle or wavelength, are related
to the physical properties of the aerosols themselves. This implies
that it should be possible to obtain numerical estimates of the parti-
culate size distribution and columnar mass concentration from measure-
ments of the absolute diffuse intensity and its gradient near the sun.
As it happens, the analysis methods used to relate measurements of
sky aureole intensity to aerosol parameters are most accurate when
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applied to atmospheres of low turbidity. This means that photometric
measurements of the solar aureole may be used to study the properties of
aerosols in atmospheres of small optical depths where the aerosol
content is hardly even detectable by other methods. Thus, the aureole
method has the advantage that one may deduce the characteristics of the
aerosols directly without disturbing or altering them in any manner. In
addition, the method relates to total aerosol content in the atmosphere,
integrated over height, and the properties are less affected by local
surface conditions and more representative of the background conditions.
The inherent disadvantages of direct sampling methods are thus avoided.
The Relation Between Aerosols and Global Climate
One of the reasons for studying the background aerosols is related
to their important role in the regulation of global climate. Rasool and
Schneider (1971), for instance, estimated that if the average global
aerosol optical depth were to increase, a net cooling of the earth's
surface would result which could, if the aerosol loading were suffici-
ently large, trigger an ice age. It has since been pointed out by
several investigators (Mitchell, 1971, for example) that the effect of
aerosols on climate is complex, and in fact a net heating or cooling may
result depending upon the particle composition and size distribution, as
well as other physical parameters such as the particulate height distri-
bution and optical and thermal properties of the underlying surface.
It is a disturbing fact that rising industrialization around the
world may eventually generate enough particulates to affect the climate.
A case in point is the possibility of climate change brought about by
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a stratospheric layer which might be created by large fleets of super-
sonic transport aircraft flying in the stratosphere. Although the opti-
cal depths involved in such a layer are likely to be small, the material
is distributed globally because of stratospheric winds and diffusion
processes. Hence the effects would be widespread, and may alter the
radiation matrix at places as remote as the polar regions which are
thought to be particularly sensitive to changes in radiation clima-
tology (Fletcher, 1965). It is therefore all the more important to
establish a baseline of global aerosol distribution as rapidly as possi-
ble.
Photometry of the solar aureole allows one to determine two para-
meters that are relevant to possible climate changes caused by aerosols:
the aerosol size distribution, and the aerosol columnar mass loading.
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The Brightness or Intensity of the Day Sky
If the atmosphere were free of aerosols, the sky intensity would be
nearly constant with angle near the sun, and no major brightness gradient
would be associated with the location of the solar disk itself. In
other words, if one were to blot out the sun with an occulting disk and
inspect the diffuse sunlight around the disk, one would find, in the
case of an absolutely pure atmosphere, a smoothly varying gradation in
sky intensity. The sky near the sun would be deep blue and relatively
homogeneous (Figure 1). However, observations of the diffuse sky in-
tensity have never documented such homogeneous sky conditions up to
within a degree or so of the solar disk. Instead, it is more usual to
find a strong whitish glow of light around the sun with a steep bright-
ness gradient typically falling off rapidly with increasing angular
distance from the sun (Herman et a!., 1971) (Figure 2), but sometimes
having more complex structure with hints of ring phenomena. Occasionally,
the aureole has colors associated with it, although the hues are generally
poorly saturated and subtle. The angular dimension of the aureole
varies from place to place, and at any given location there are temporal
variations, with significant changes in form and intensity sometimes
occurring in time periods of less than one hour.
Generally speaking, the solar aureole is difficult to view with the
unaided eye, partly because of its inherent brightness; but more im-
portantly because of the overwhelming brightness of the direct sun.
With some experience, however, one can learn to observe the aureole by
blocking out the sun with a distant tree or pole, for instance, and
inspecting the region around the sun through a neutral density filter
with a transmissivity of about 10 percent. Using this technique, and
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r=0.15 A=0.0
ISOPHOTES IN ITT
o
30*
150<
120<
180
Figure la Polar plot of sky intensity for a molecular atmosphere.
Intensity is expressed in units of solar flux divided
by IT.
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S-
fC
o
OJ
o
E in
i/>
OJ 0)
.c s-
(-> JT
-I-J
00 CD
c: s_
OJ OJ
4-> -C
c CL
r- 1S
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APRIL 26,1974 COLLEGE, ALASKA X=500nm
0°
^ 30°
60<
120*
150'
Figure 2 Polar plot of sky intensity as observed at Collge, Alaska
on April 26, 1974 at 500nm. Sky radiance =ir!/Fo.
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making careful observations during clear periods, the aureole can be
seen to vary from time to time and and can be placed into one of several
classifications based on color, size and brightness. Such observations
are highly subjective, however, and it is a distinct necessity to develop
and use instrumentation particularly adapted to the problems and pur-
poses of solar aureole measurements.
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THEORY OF RADIATIVE TRANSFER IN A TURBID ATMOSPHERE
General Remarks on the Theory
In order to discuss the observational results which will be pre-
sented, we must first develop some theoretical background. In parti-
cular, we wish to address ourselves to the problem of specifying the i
Stokes component of radiation field, I, of scattered light in a turbid
atmosphere, (e.g., an atmosphere containing particulate material il-
luminated from the top by parallel radiation). For the sake of simpli-
city, we shall assume that the atmosphere can be approximated as being
plane-parallel and infinite in extent and horizontally homogeneous.
This approximation is valid, provided that both the elevation angles of
the source of radiant energy (the sun), and the direction of view in
which one requires the radiation field to be specified, are larger than
approximately ten degrees or so. The geometry of the situation is
illustrated in Figure 3.
The i Stokes parameter of the radiation field, I., may be ob-
tained by solving the equation of radiative transfer (Chandrasekhar,
1950) which, for a plane parallel atmosphere, can be written as,
dl . (T ,u ,<{>) ^
1 _ T / , \ , (1)
0 j U
where p=cos z, with z being the zenith angle of the direction of view at
which the radiation field is to be specified (\\ is positive for downward
directed radiation); z is the direction of the incident solar radiation,
is the corresponding azimuthal angle referred to the sun's azimuth,
0)
-------
O)
4-
l/l
to
S-
-a
rO S-
-!-> O
O (O
O O)
I r
4-> r
3 03
O (O
(/) Q.
M rd
c i
re CL
>
O)
OJ r
E -Q
O O
O) S-
CD Q.
CO
0)
s_
Z3
cn
10
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represents the albedo for single scattering, F is the Stokes vector of
the incident flux,and P. is the normalized Stokes scattering matrix (van
de Hulst, 1957) for the particular atmospheric scattering media.
The parameter, T, is a quasi-monochromatic optical depth defined as
T(h) = { [3abs(h) + Bsc(h)]dh 2)
here e , and 6 are the volume absorption coefficient and the volume
aos sc
scattering coefficients respectively, evaluated for a sample of the
atmospheric media at height h.
The Stokes scattering matrix for a volume of the scattering medium,
P(e), is evaluated at scattering angle e (see equation B7 in appendix
B) and each element is normalized according to
P.(e)du - 47T 3)
1
where dco represents a differential solid angle, and the integration ex-
tends over 4-rr steradians.
b
The optical depth, T, the albedo of single scattering, w, and the
scattering phase function, P., depend upon the physical nature of the
gases and particulate material contained in a representative volume
sample of the atmosphere medium at height h. In practice, one evaluates
these optical parameters separately for the molecular gas (the Rayleigh
component) and for the participates. The optical parameters for inter-
action of radiant energy on particulate material are generally evaluated
by assuming that the particulates contained in a volume of air can be
approximated by an ensemble of spherical particles distributed over a
range of particle radii as specified by the particle size distribution
function i|;(r). The theory describing the electromagnetic scattering
from an ensemble of spherical particles was first formulated by George
11
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Mie in 1908. A brief description of Mie's scattering theory was given
by van de Hulst (1957).
A turbid atmosphere is not homogeneous with respect to its scat-
tering properties; that is, each element of the scattering matrix must
be written in the weighted form (Deirmendjian, 1970),
3SCR PR(e) + eSCM PM(e)
where the subscripts SCR and SCM refer to scattering portions of the
volume extinction coefficient for gaseous molecules (Rayleigh component)
and for particulates (the Mie component). PR and PM are the "Rayleigh"
and "Mie" scattering phase functions at height h in the atmosphere. In
addition, for a volume of turbid air, Deirmendjian points out that the
effective albedo for single scattering is given as,
^ = BSCR + BSCM
^
+0+0+
PABSR ^SCM
where 3ABSR and 3ABSM are the absorption components of the "Rayleigh"
and "Mie" extinction coefficients respectively. The resultant albedo,
w is dependent on the type of scattering particle.
Primary-Scattering Atmosphere
It will be useful for our purposes to consider an approximate so-
lution to the equation of transfer for a turbid atmosphere where only
primary scattering is considered. This means, effectively, that we
assume the integral term in Eq. 1) to be negligibly small. In addition,
one assumes that u> and P are, to a first approximation, independent of
height, and Eq. 1) may be integrated directly to obtain the first-order
scattering term of the Stokes parameter, I., as,
12
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Equation 6 neglects high-order scattering effects and we re-em-
phasize that it therefore represents only an approximate solution to the
radiative transfer processes in the atmosphere. There are certain
instances, however, where one may justifiably employ a single-scatter
model to describe the diffuse radiation field. The accuracy of the
model's predictions of the radiation environment increases as total
optical depth diminishes, and in the limit -r>0, the approximate single-
scatter solution becomes exact. The accuracy to which Eq. 6) approxi-
mates a "true", or exact, solution also depends on the magnitude of the
solar elevation angle, and less obviously, on the form of the scattering
phase matrix. A practical example showing where one might utilize the
single-scatter model to predict the diffuse radiation field can be found
in areas requiring sky polarization and intensity prediction at aircraft
or rocket altitudes where the optical depth remaining above the observer
may approach small values (i.e., i<^0.1). Another example, and one that
is more relevant to the problems at hand, involves the use of a single-
scatter model in the interpretation of sky radiance in the red and near
infrared regions of the electromagnetic spectrum, between gaseous ab-
sorption features, where optical depths are small (i.e., TD = 0.04 at
K
A = IP). In this regard, it is assumed of course that optical effects
for aerosols can be ignored. In other words, the results would be
expected to be valid only in the case of extremely pure atmospheres such
as may be found over the polar regions, for instance. However, as will
be demonstrated later, it is likely that such an assumption is rarely
met in practice, and that in fact the optical effects arising from even
13
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minute aerosol loading can be of great importance in the radiation en-
vironment. Nonetheless, from a pedagogical point of view, it may be of
value to compare results of predictions of a single-scatter model (i.e.,
Eq. 6) with those obtained by exact solution of the equation of transfer
including all orders of scattering. In this regard, techniques have
been described by Chandrasekhar (1950) for solving the transfer equation
exactly for a Rayleigh-scattering mechanism. Coulson, Dave and Sekera
(1960) implemented Chandrasekhar's solution and compiled the results of
the solution in tables for various numerical values of optical depth, T,
ground albedo, A, solar zenith angle, y , observed zenith angle, z, and
relative azimuth, .
Figure 4 shows a comparison of sky intensity as obtained by using
the single-scatter approximation (Eq. 6), (dotted line) and as obtained
from Coulson et^ aj_. 's tables. Curves are shown for a ground albedo, A,
equal to 0.00. Parameters in Figure 4 are as follows: T = 0.05, u=p =0.4.
The curves in Figure 4 refer to the solar vertical plane. Note that the
single-scatter approximation is reasonably close to the actual true
radiation values as predicted by Coulson j^t aj_.'s tables, except for low
elevation angles, near the horizon, where the results diverge.
One must remember that the single-scatter approximation to the
solution of the equation of transfer is indeed only an approximation to
the true radiation field, and high-order scattering can in fact make
a significant contribution to the total radiation field. In general,
the contribution of multiple scattered radiation becomes more important
near the horizons,and relatively speaking, it also becomes more im-
portant as the optical depth increases above approximately 0.1.
14
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ai
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15
-------
In view of the fact that optical depths for realistic atmospheres
in the mid-visible are of the order of T=0.15, the effects of multiple
scattering can not be neglected if high accuracy is wanted, and it is
advisable to incorporate, by some method, the effects of multiple scat-
tering in a model of the circumsolar radiation. This is done by con-
sidering the effect of the scattering by aerosols as a perturbation on
an equivalent Rayleigh scattering mechanism which, as we have already
pointed out, has been solved for all orders of scattering (Coulson ^t_
aj_., 1960). As we will see, this method of treating the effect of
aerosols as a perturbation allows one to devise a useful and relatively
simple method for use in quantitatively interpreting the circumsolar sky
radiation.
16
-------
THE EFFECT OF AEROSOLS TREATED AS A PERTURBATION
ON THE RAYLEIGH SCATTERING MECHANISM
If one neglects high-order scattering, and considers primary scat-
tering only, then one may solve two separate equations (one for aerosol
scattering and one for molecular scattering), of a form similar to Eq.
1, but excluding the integral term. A solution is then obtained by
adding the individual Rayleigh and Mie components. However, this technique
would be rather unrealistic, because solutions to the equation of trans-
fer exist, including all orders of scattering, for a Rayleigh scattering
phase function. In view of this, a more reasonable approach is to
incorporate the total Rayleigh solutions as tabulated by Coulson et al.
(1960), and treat the effect of the aerosols as a perturbation on the
Rayleigh scattering mechanism. To do this, we follow Deirmendjian
(1970) who shows that the i component of the scattering matrix, P.(e),
for a sample of turbid air, may be written in the form (essentially
equation 4 in a different form),
n
p(e) = p(9> + (p(e) - p(e)) 7)
where, in the strictest sense, 3crD and 3crM, and therefore P. (e) are
oLK oU"! i
functions of height, h. Notice that the multiplier of the second term,
the turbidity coefficient 3criv|/(£cpD+3crMK vanishes when the aerosol
loading becomes negligibly small, a desirable characteristic for a
"perturbation" scheme.
When the scattering matrix (Eq. 7) is introduced into the equation
of transfer (Eq. 1), the resultant equation can be expressed as the sum
of two separate equations, written for the Rayleigh component, ID, and
K
the perturbation component, I Each of these equations may, at least
in principle, then be solved and the field can be obtained by simple
17
-------
addition of terms. The tabulation of Coulson ^t al_. (1960), for example,
can be used, appropriately interpolated, to obtain the solution ID.
K
The equation for the perturbation component, In, has been derived
by Deirmendjian (1970), and the result is,
8)
[PD(8)
[PR(9)
where f(T) = ^CN/^SCR + 3SCM^' PD = PM " PR' and e 1S the Scatterin9
angle between the directions z', ' and z, 4>.
As Deirmendjian points out, Equation 8 is amenable to solution in
various approximations, depending upon the particular aspect of the
problem of interest. For instance, one can disregard the integral term
which is equivalent to neglecting high-order scattering effects which
arise from the aerosols. The resulting equation will yield a first-
order approximation which accounts for primary scattering according to
the virtual phase function P~ = P.. - PR. In a clear atmosphere with
low turbidity, this approximation should be most suitable for estimating
the radiation field in the vicinity of the sun within angular distances
up to approximately 40°. Deirmendjian indicates that the effects of
turbidity on the sky light at larger angular distances from the sun is
such that the integral terms in Eq. 8) cannot be neglected anymore. One
could, of course, utilize an iterative method and obtain a first-order
approximation to the perturbation field, I., by the technique just
18
-------
described, after which the solution could be substituted in the integral
(2)
expression in Eq. 8) to obtain a second-order approximation, IDV '. The
procedure, which is somewhat tedious to carry out, could be continued in
an iterative fashion until the trial solutions agreed with the calculated
solution to within some pre-specified accuracy criteria. In any event,
the total field representing the sky radiation in a turbid atmosphere,
would then simply be,
I(T',ZO,Z,C|>) = IR(T',ZO,Z,<|>) + ID(T',ZO,Z,
-------
with homogeneous turbidity which means that we replace the actual verti-
cal distribution by a virtual distribution with a constant mixing ratio
of particle to molecules, so that the total numbers in a vertical column
remain unchanged. In other words, we set,
6SCM(h) T'M
= ~ 1 ~ = Constant 11)
0
3SCR SCM R
The substitution of Eq. 11 into Eq. 10 results in,
I H)(T, } _ (PM - PR} r sec(z)
D u 'zo'z; 4,7 ho Tsec(z) - sec(z0)|
e-T'sec(zQ)_e-T'sec(z)
Notice that the Eq. 12) is identical in form to the solution of the
equation of transfer for single scattering (Eq. 6), except that it is
multiplied by a turbidity factor equal to TM/(TM + TR), and it employs
a virtual phase function (PM -PD).
rl K
Deirmendjian points out that the simple first-order solution (Eq.
12), should be used only when one is interested in a) the radiation
field at the bottom of the atmosphere and b) values of z and z less
than approximately 80° so that the effects of the curvature of the
atmosphere do not invalidate the initial assumption of a plane-parallel
atmosphere.
20
-------
INSTRUMENTATION
Direct Sun Photometer
In order to assess atmospheric aerosol parameters using sky intensity
measurements one must know the optical depth of the atmosphere, T-J-(A).
This parameter was determined in this study by using a battery operated
photometer which was constructed to measure the ground-level solar flux
at narrow wavelength intervals; it is shown in Figure 5. The photometer
uses interchangeable 25mm diameter interference filters to define wave-
length intervals typically about lOnm wide. The optical head of the
device consists of a 30mm diameter, 200mm focal length, objective lens,
a field aperture and a solid state silicon photodetector. The field
aperture is used to define a 3° diameter field of view. In use, the
optical head is pointed at the sun with the aid of a small peep sight.
The electric current from the photodetector is amplified with a
feedback-controlled operational amplifier circuit. The schematic
diagram of the electronics is shown in Figure 6.
The feedback resistors are a carbon film type to minimize resis-
tivity changes with temperature. The unit employs an FET input high
impedence operational amplifier with an input bias current less than 1
pa.
The planar photodetector is operated in an unbiased photo voltaic
mode with a temperature coefficient of about 0.1%/°C. There are five
ranges of sensitivity each differing by a factor of ten times from its
adjacent position. On maximum sensitivity, full scale deflection is
_c _p -I
provided by a radiant flux (at A = 500nm) of 2 x 10~ yw crrT nm~ from a
21
-------
*
Figure 5 Photograph of the direct-sun photometer.
22
-------
NT
tto
o
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CVJ
UJin
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-------
point source. If the source is diffuse, a uniform intensity of 6.5 x
-2 -2 -1 -1
10 yw cm nm sr will give full scale reading on the most sensitive
scale. Minimum detectable signal is roughly equal to 1% of the most
sensitive scale which corresponds to a value of intensity (at A = 500nm)
of 6.5 x 10" uw cm" nm~ sr~ .
In order to use the instrument to measure direct solar radiation,
we employ a reduced aperture with a diameter of 0.5mm to limit the in-
coming radiant energy.
Calibration of Sun Photometer
A 200 watt quartz iodine lamp powered by a regulated constant-
current source (Stair, Schneider and Jackson, 1963) is used to calibrate
the sun photometer. During the calibration, one must use extreme care
to insure accurate results; we have heard many reports of standardized
lamps suddenly changing irradiance. To insure against this eventuality,
we intercalibrate among three separate standard lamps; this procedure
increases the confidence of the calibration and it is highly recommended
as a standard calibration procedure. It is also important to have a
constant current supply because lamp radiance is especially sensitive to
current variations. The lamp housing is also a matter of some impor-
tance; ideally it should consist of a dead black surface with no in-
ternal reflections and an adequate air supply to prolong lamp life. One
must check against reflections from walls, ceilings and components
within the calibration room. We use a room that is specially designed
with extensive baffling to reduce spurious reflections.
The calibration for radiant flux is carried out by pointing the
photometer at the standard lamp. Because radiant flux decreases ac-
24
-------
_o
cording to r , one can, by varying the photometer-lamp distance, adjust
the incoming flux over known relative ratios; this provides a method of
checking photometer linearity. In this fashion we have experimentally
determined that the sun photometer output voltage is linearly related to
the input radiant flux to better than one percent over a range of four
orders of magnitude of input radiance.
The photometer can also be used to measure diffuse radiation (in-
tensity) but the calibration procedure is slightly different. For this
case, one views a white Lambertian screen (Figure 7) that is directly
illuminated by a point source of light (a 200 watt quartz iodine stan-
dard lamp).
Accuracy requirements of optical calibration are important. As an
example, we consider the precision necessary for calibrating a sun
photometer. If one assumes that a negligible amount of diffuse radia-
tion enters the field of view of the photometer in comparison to the
direct solar flux, then, for a linear instrument, one may write the
Lambert-Beer extinction law in terms of photometer voltages as
,1
-r(A)-sec(zJ
V(T,A) = V'(A) e u 13)
where V(T,A) represents the measured photometer voltage resulting from
direct solar radiation attenuated by an atmosphere of optical depth T(A).
The term V (A) is the estimated photometer voltage that would arise in
the absence of an attenuating atmosphere. This term can be derived
through a standard lamp calibration method provided one knows the value
of the solar spectral radiance and the lamp spectral radiance at wave-
length A. The value of V can also be derived by extrapolating direct
sun photometer measurements made at different values of solar zenith
25
-------
O)
-M
01
O
-(->
O
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CL
(/I
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cn
26
-------
angle z, through the atmosphere; that is to say, a point where r-sec(z)
equals zero. Either way can be used, and in practice we have found that a
combination of the two methods, using solar radiation measurements only
for the clearest days, gives the most accurate results. Once V is estab-
lished, variations in V caused by photometer aging can be assessed by
monitoring, upon occasion, the standard lamps. In this way one can periodi-
cally update the so-called intercept voltage, V , to take account of long
term drifts in photometer sensitivity.
In any event, the value of V , for a given photometer, is built up
from the results of sun and standard lamp measurements, and any errors,
caused by inaccuracies in T or by temporal variations in T during the
times the direct sun measurements are being accumulated. Assuming that
the photometer voltage, V(T,X) is measured with perfect accuracy, what
then are the requirements on V , and thus calibration accuracy, if we
want to know T to some stated accuracy? This is easily assessed by
differentiating equation 13 to give
= dV](A)e ° - V](A)e ° dx/M0 14)
As a numerical example, if we wish to determine T to an absolute
accuracy of 0.010, for y = 0.25 (z=75.6°) one will require that
dV /V be known to within 0.04. This accuracy is difficult to obtain
by optical calibration methods, but it is certainly possible provided
one makes every effort to assess and to minimize optical calibration
errors.
27
-------
Photoelectric Coronameter
It is difficult to make accurate measurements of sky radiation
close to the sun because of problems with instrumental scattering and
diffraction from the bright solar disk just outside the field-of-view of
the instrument. In practice, one must utilize special techniques to
reduce these instrumental effects when attempting to make photometric
measurements closer than approximately five or ten degrees from the
solar limb. Recall that these measurements close to the sun are in fact
extremely important for our purposes because the sky brightness in this
region is highly dependent on the aerosol content of the atmosphere.
Because of this, we devoted considerable attention during this study to
designing an instrument which could be used to measure sky intensity
close to the sun's limb. The resultant instrument uses a photoelectric
detector and in many respects is similar to a solar coronagraph (Eddy,
1961; Evans, 1948).
Figure 8 illustrates, in a schematic way, the construction of the
photoelectric coronameter. The design is similar to a visual sky bright-
ness photometer described by Evans (1948). Its operation may be ex-
plained as follows:
Light from the region of the sky surrounding the sun passes through
aperture a-,. Filter f, defines a narrow wavelength interval for the
observations. The direct radiation from the solar disk is blocked from
entering aperture a-, by the occulting disk 0-,. In other words, the disk
0, is made large enough so that no portion of the solar disk can be
"seen" from any point in a,. Lens L, forms an image of the sky around
the sun at the field stop. Aperture a? and occulting disk 02 define an
annular field of view.
28
-------
a:
ui
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29
-------
Diffracted light from around 0, is prevented from entering through
the system by making occulting disk 0? large enough to block the slightly
out of focus image of 0,. Lens l_2 in conjunction with lens L-, forms a
low power (2.5X) telescope. When viewed through Lp, one sees an in-
focus image of the backside of occulting disk 0? surrounded by an image
of the sky around the sun.
Although primary diffracted light emanating at the edge of oc-
culting disk 0, has been suppressed, there is yet another source of
diffraction, namely the edges of the entrance aperture a,. This source
of diffraction is eliminated by placing aperture a,, slightly smaller
than the exit pupil of the telescope system, at the image of a, formed
by lens L^. The light rays passing through the aperture finally impinge
on a PIN-doped silicon photodetector, PD, to generate an electric cur-
rent which is amplified and registered on a panel meter or chart re-
corder.
The diameter of a? and 0^ in conjunction with the focal length of
lens L, determine the inner and outer angular diameters of the annular
field of view from which sky radiation is accepted. In the instrument
designed for this study, we employed two optical systems designed to
accept radiation from two regions of the sky corresponding to two dif-
ferent scattering angles. Figure 9 shows the details of the field stop
that is located at the focal point of lens L,. As already mentioned,
the instrument has two optical paths; one accepts radiation from an
annular region (A). The other channel accepts radiation from the partial
annular region (B). The areas A and B are equal so that if there were
no brightness gradient in the aureole, the radiant flux passing into the
two apertures would be equal.
30
-------
CO
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h-
Q_
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I
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31
-------
Behind the aperture A and B there are two cylindrical "eyepiece"
assemblies each containing lens elements (L,,) and apertures a^. The
photodetector, PD, is in a removable mount which can be placed over each
"eyepiece" assembly to obtain a measurement. Notice that the "eyepiece"
assembly which receives light from aperture A, is on axis with a line
drawn from the sun to the entrance aperture a,. The "eyepiece" assembly
that receives radiant flux through the optical path marked "B" in Figure
8, however, is canted off along a line drawn from L-, through the mid-
point of aperture B. It may be noted that when the photodetector unit,
PD, is removed, one may directly view the solid angle of the sky from
which radiation is being accepted. This is useful to insure that the
optics are properly aligned and also to insure that nothing is blocking
the field of view. Figure 10 shows the optical housing of the corona-
meter.
In use, the instrument must be pointed accurately at the sun. This
is done by centering the shadow of the occulting disk on the entrance
aperture. The front portion of the instrument is supported on a camera
tripod. The elevation angle is changed by cranking the center post of
the tripod and azimuth angle is adjusted with a rack and pinion on the
head of the tripod.
The coronameter is portable and easy to set up in the field. Total
weight including tripod is about 10 kg.
Relevant instrument parameters are listed in Table 1.
Table 1
Photoelectric Coronameter Specifications
Diameter of primary occulting disk 0, 19mm
Diameter of entrance aperture a, 3mm
Separation of 0-, and a-, 1000mm
32
-------
*>v ;,* * * y^*r;
*^;t »* fr' »«*'*;" / >* .,**C "S
t't-«t" *«*» 1? V *,.** :" i. » *
-------
Focal length of objective lens L-, 250mm
Focal length of field lens L~ 100mm
Diameter of exit aperture a^ l.lmm
Photo detector Silicon, PIN-doped
Mean Scattering Angle (Chan. 1) 1.1° (from solar limb)
Mean Scattering Angle (Chan. 2) 6.2° (from solar limb)
The two channel design allows one to evaluate quickly and easily
the scattered sunlight at two different scattering angles from the solar
limb. These two data points are supplemented with readings of sky in-
tensity made with a sky photometer that is equipped with a well-baffled
collimator and is used for scattering angles larger than ten degrees.
Calibration
The photoelectric coronameter is calibrated by pointing it at a
diffuse Lambertian screen placed exactly perpendicular to the sun and
illuminated by the direct solar radiation. The illumination of the
screen by the direct sun and sky may be written as,
R,
SC
F ' T
o 'ATMOS
= Hi f f,,c
S + D
cos(e12) dw 15)
-2 -1 -1
where I<- = diffuse screen intensity (yw cm~ nm~ sr~ ) resulting from
direct radiation, S, plus diffuse radiation, D
S~ = Hemispherical screen reflectivity (0.99 at A = 0.5y)
2 -1
F = Incident solar flux (MW cm" nnf )
= Slant path atmospheric transmission evaluated at mean ob-
servation wavelength
= Diff1156 "incoming sky intensity
e,p = Angle between solid angle cone, du, and direction to sun.
The integration is carried out over the hemisphere above the screen.
34
-------
This integral term represents the component of screen intensity due to
the illumination of the screen by the diffuse sunlight and reflected
ground radiance. In clear atmospheres it is typically about one tenth
as large as the first (direct solar radiation) term.
In practice, the transmission of the atmosphere, TATMOS, is de-
termined by measuring the direct incoming solar flux with the sun photo-
meter, as described in the proceeding section.
The second term in Eq. 15 corresponding to the component of screen
intensity due to illumination by diffuse light is accounted for experi-
mentally by blocking out the direct component of solar flux and allowing
the screen to be illuminated by diffuse radiation only. By measuring
photometer current arising from the screen when illuminated by direct
sun plus "diffuse" sky, Ic+n> and then subtracting the current which
arises from the screen when it is shadowed from direct radiation, one
may infer the photometer current which would arise from direct solar
radiation alone, i.e.:
which, in turn, allows one to derive an expression for the calibration
constant of the instrument,
(IS+D - in) T
C = p F-^f - = amperes/intensity unit. 17)
KSCV ATMOS
Typically, the calibration gives a day-to-day repeatability to better
than about 5%. When the instrument is taken from a room temperature
environment and used in very low temperatures (T = -30°C), an insigni-
ficant shift in calibration of a few percent is found to occur, probably
35
-------
due to slight changes in the optical alignment. We have used the in-
strument over a range of air temperatures -35°C < T < 40°C with a total
change in calibration of less than five percent.
36
-------
RESULTS AND DISCUSSION
Overview
During the period extending from February, 1973 to the time of this
writing (June 1974), we made numerous measurements of sky intensity and
atmospheric transmission. Only a small sample of the data taken, how-
ever, are illustrated here. One reason for this is that only a few
measurements are necessary to demonstrate the general technique used;
another reason is that the quality of the data improved steadily as the
instruments and methods of data acquisition were improved. Emphasis is
therefore directed toward the more recently acquired data.
As we have mentioned previously, the perturbation method of anal-
ysis is most useful and should therefore have the greatest application
for studies involving clear, homogeneous atmospheres. As a result, we
have made the great majority of our measurements at times when air
purity was high and when urban contamination was negligible. In other
words, we directed our efforts towards assessing the "background"
aerosol.
We have made measurements from the following locations: in Alaska,
at Ester Dome, Alaska (64°53'N, 148°03'W); from the roof of the C.T.
Elvey building on the "west ridge" of the University of Alaska campus at
Fairbanks (64°52'N, 147°51'W), and from the NOAA Geophysical Monitoring
Site at Barrow, Alaska (71°19'N, 156°37'W). In addition, we have mea-
sured sky intensity at Tucson, Arizona at The Institute of Atmospheric
Physics (32°14'N, 110°57'W) and from an equatorial location at Loiyen-
galani, Kenya (2°45'N, 36°42'E). Eventually, we hope to make sky inten-
sity measurements at the NOAA background monitoring station at Mauna Loa
to intercompare with existing radiation measurements that are being
gathered there.
37
-------
Measurements on April 11, 1973
The course of sky intensity and sky polarization is illustrated in
Figure 11 for April 11, 1973 at Fairbanks. The curves correspond to sky
intensity at a mean wavelength of 500nm in the solar vertical plane
(solid) and the solar almucantar (dotted). The measurements were made
with an early version of a sequence of several sky photometers. We
learned, unfortunately after the measurements were taken, that this
photometer in its early design had a calibration uncertainty and as a
result, the ordinate values cannot be expressed reliably in absolute
units, instead the ordinate scale is in relative units normalized to 1.0
at the zenith (Note that a logarithmic scale is used).
The conditions during the measurements of Figure 11 were as fol-
lows: the sky was clear of clouds and the snow cover was approximately
50%. A measure of the ground albedo gave Ap..., = 28%. Horizontal
visibility during the measurements was judged to be approximately 160
km (the Alaska Range at a distance of 144 km could be seen with
medium contrast). The summit of Mt. McKinley (d = 240km) was not visible.
The curves displayed in Figure 11 show, qualitatively speaking, the
features that one might expect for a relatively pure atmosphere. A
polarization maximum occurs at a primary scattering angle of approxi-
mately 90°. A minimum in intensity is seen at approximately 87 from
the sun. A marked aureole is present and extends out several tens of
degrees from the sun.
Measurements on May 1973, at Interior Alaska
Figure 12 illustrates sky brightness at two wavelengths (500nm and
700nm) in the almucantar on May 3 and 4, 1973. Conditions on May 3 were
38
-------
20.0
i10-0
^ 5.0
c/)
3 2.0
o
i.o
0.6
60
° 40
20
00
O
1 1
n r
n r
APRIL 11, 1973 AM
COLLEGE, ALASKA
-SOLAR VERTICAL
= 0.51 ,
T = 500 nm
I j i i i i I I I I I
SKY POLARIZATION
1 1 n
I I i
60° 40° 20° 0 -20° -40° -60°
ZENITH ANGLE, Zo
Figure lla Sky intensity on April 11, 1973 at College, Alaska at
500nm. Normalized to 1.0 intensity unit at the zenith,
Figure lib Sky polarization ratio in solar vertical plane.
39
-------
I I I I I I I
I I
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as follows: horizontal visibility, 225km; air temperature, 18°C; wind,
from E at 7 m/s; sky cover less than 5% cirrus. Slight mottling noticed
near horizons. The data in Figure 12 were acquired with a collimator
photometer, MKI, which was later superseded by a more carefully designed
model with better baffling. Again, as in Figure 11, the ordinate scale
intensities are normalized, in this case to 1.0 at 5 azimuth from the
sun. Figure 12 also illustrates similar data for May 4, 1973, from the
C.T. Elvey building in Fairbanks. Visibility, 250km; temperature,
23°C; wind, 12 m/s from N.E. The aureole brightness gradient is slightly
smaller on this day in comparison to May 3 (Figure 12).
Measurements During Forest Fire Episode-July, 1973
Figure 13 shows measured (solid) sky intensity (in absolute in-
tensity units) in the solar almucantar (Figs. 13a and 13b) and in the
solar vertical plane (Figs. 13c and 13d) on July 25, 1973, during a time
when an intrusion of smoke had penetrated into interior Alaska from
forest fires which were burning at the time in Eastern Siberia. Curves
are presented for mean wavelengths of 500nm (green) in Figures 13a and
13c and 700nm (far red) in Figures 13b and 13d. Figures 13a and 13b
refer to the solar almucantar, and Figures 13c and 13d refer to the
solar vertical plane. The optical depths, measured with the sun photo-
meter, during the period were: TT(500nm) = 0.360, xT(700nm) = 0.190.
Subtraction of the components arising from Rayleigh scattering and ozone
absorption (Elterman, 1968) yields the following numerical values for
aerosol, or Mie, optical depths: TM(500nm) = 0.214, and TM(700nm) = 0.146.
In Figure 13, we show curves of sky intensity (dashed-lines) that
would result from a pure Rayleigh-scattering atmosphere with no contamination,
41
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4->
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4J
O.
X
Ol
QJ
o
13
O)
00
O)
s_
3
( JS UUU OIO
| I " O
45
-------
i.e., T=TDavie-jah' These curves were extrapolated from the tables of
Coulson et^al_. (1966) and include effects of multiple scattering and
surface reflectivity. The dotted curves correspond to an atmosphere
having optical depth equal to the total observed (Mie plus Rayleigh)
optical depth on July 25th and scattering in accordance to the Rayleigh
scattering mechanism. It is obvious that this theoretical curve is a
better approximation to the observed sky intensity in Figure 13. The
observed intensity is larger than the equivalent Rayleigh atmosphere for
relatively small scattering angles, but smaller at larger angles. This
implies that the aerosol scattering function P(0), is strongly "peaked"
in the near-forward direction and the deficit radiation at large scattering
angles (where IQu < IT ) is compensated for by enhanced scattering
in the forward directions. Qualitatively, a strongly peaked phase
function is consistent with the hypothesis of scattering from a volume
of air containing aerosol particles that have sizes "of the order" of
the wavelength of the illuminating radiation.
A value of surface albedo equal to 0.15 was used to obtain the
calculated curves in Figure 13. This value seems reasonable for the
conditions that existed at that time, namely full vegetative growth of
mixed coniferous forests and scrub black spruce interspersed with low
brush and clear areas.
To support the value of A = 0.15, we made measurements of surface
albedo from the roof of the Elvey building on July 25, 1973. During
these measurements, the solar elevation was within five degrees of its
value for the sky brightness data shown in Figure 13. Table 2 shows the
averaged results.
46
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Table 2
Values of surface albedo measured at College, Alaska
Type of surface Albedo at SOOnm* Albedo at 700nm*
(percent)(percent)
Coniferous forest 3% 7 to 9%
Green freshly cut lawn 5% 10 to 12%
Dead grass 10% 20 to 24%
Asphalt Pavement 6% 22%
*Albedo values are with respect to a perfect horizontal Lambertian
reflector.
The atmospheric sky intensity in Fig. 13 is substantially larger
than theoretical predictions based on a Rayleigh atmosphere; the dif-
ference of course is due to scattering by aerosols, which were smoke
particles in this case.
The data illustrated in Figure 13 were taken with a photometer with
a collimating tube containing many baffles. The calibration procedure
which is required to convert the raw voltage readings into radiant
absolute intensities has been described in a previous section. The
calibration constant for the instrument is considered to be accurate to
within one or two percent at large angles from the sun; but degrades
slightly for measurements taken closer than approximately fifteen de-
grees from the sun due to the extraneous light that enters the optical
system from diffraction of sunlight at the entrance aperture and baffles.
Meteorological conditions during the observations of July 25,
illustrated in Figures 13a through 13d, were as follows: temperature,
+22°C; wind from E at 7 m/s; mean solar elevation, 37°; horizontal
visibility estimated at 20km. The sky was clear, but the horizon was
indistinct; the sky near the horizon appeared yellowish-brown and the
47
-------
air quite obviously smokey. Visually, the aureole around the sun appeared
much larger than usual and brighter, although these observations of
aureole appearance are quite subjective.
The aerosol scattering phase function, P(e), was derived from the
curves in Figure 13 by the perturbation method described previously.
Figure 14 illustrates the phase function (heavy line) so derived.
Notice that the scattering phase function has a smooth monotonic shape
with little indication of diffraction ring phenomena such as one might
find if the aerosols were mono-disperse. Computed phase-functions for
aerosols distributed with a Junge power-law distribution are shown for
comparison (deBary et_ aj_., 1965). Although the observed curve does not
match any of the "computed" curves exactly, there is reasonable agreement
to the curve computed for Junge exponent value, v, equal to 4.0. One
can, in any case, state that there is a tendency toward the larger
(i.e., v=4) values of v.
In view of the various inaccuracies that come into play (such as
instrumental diffraction, uncertainities in ground albedo, and the
deviation between an exact solution to the equation of radiative trans-
fer and the approximate solution based on first-order perturbation
theory), one is probably not justified in trying to obtain more exact
matches to P(o) curves computed for more complex aerosol distribution
functions.
The scattering phase function, P(e), on July 25th corresponds to
scattering mostly from relatively small particles because the r~^v '
dependence of the Junge size distribution function implies relatively
smaller concentrations of giant and large particles when v is fairly
large as it is during this episode (Junge, 1963). This observation is
48
-------
100
50
c
o
"o
c
-------
consistent with the hypothesis that the aerosols derived from forest
fire smoke consist of large concentrations of particles in the r < l.Oy
size.
Aerosol Optical Depths Inferred from Sky Intensity
The aerosol optical depth, TM(A), can be inferred to some extent
from the sky intensity measurements themselves. From Eq. 12, one can
see that when PM(Q) = ^RAYI EITH t'ie Perturbation intensity is zero and
therefore the measured sky intensity should be equal to the "equivalent
Rayleigh" sky intensity computed for T=TT. When plotted together on a
2
graph, the value of the Rayleigh function, PD(e) = 0.75(1 + cos e), and
K
a typical aerosol phase function, PM(e), become about equal at a scat-
tering angle of approximately 50° (see Figure 15). The exact angle
depends, of course, somewhat on the nature of the aerosol distribution
function, but it is not as sensitive as one might expect, and P/..N =
P(D\ varies only from 48 to 55 degrees as the power-law exponent varies
from v=2.5 to v=4.0. Also shown in Figure 15 are curves for Deirmen-
djian's "haze M, L and H" (Deirmendjian, 1969).
In any event, the "crossing" of the PM(G) curve with the PR (e)
curves would be expected to occur in the range e = 45-55 for any "rea-
sonable" distribution of aerosols. One can thus immediately derive an
estimate of the aerosol optical depth, TM(A), by measuring the mono-
chromatic sky intensity in the almucantar at a scattering angle (not to
be confused with an azimuth angle) of 50° from the sun and matching to
pre-computed curves of sky intensity for a Rayleigh atmosphere as a
function of optical depth, T(A). Figure 16 shows curves of sky intensity
in the almucantar at an angular distance of 50° from the sun as a func-
tion of total optical depth. Figure 16a shows the sky intensity for
50
-------
200
100
f
47T
o
o
ID
U_
LJ
CO
X
Q_
CD
LU
O
CO
_
dr r
0.04
-------
CO
^-
UJ
CO
0 = Scattering Angle =50
ALMUCANTAR
0.1 -
°0 0.1 0,2 0.3 0.4 0.5
TOTAL OPTICAL DEPTH, TT
Figure 16a Rayleigh sky intensity, -rrl/Fo, in the solar almucantar
at an angular distance of 50° from the sun plotted against
optical depth T for three values of surface albedo, A.
Figure 16b Same as above except for four values of y .
52
-------
three values of ground albedo, A, for y=M= 0.6. Notice that one must
know the ground albedo rather accurately in order to use this method of
deducing optical depth. The curves in Figure 16 were derived from the
computed solution to the equation of transfer for a Rayleigh scattering
mechanism (Coulson et_ al_., 1966). Figure 16b illustrates the dependence
of sky brightness (at 6 = 50 in the almucantar) with total optical
depth for several different values of U=M .
One can deduce the total optical depth from sky intensity as
follows: First, one measures the absolute sky intensity in the al-
mucantar at 8=50°. Secondly, depending upon the value of y , one can
deduce TT from Figure 16. This method works best when the sun is re-
latively high (say, for example, y=u =0.6) it has important potential
applications for deducing air turbidity values at background locations
such as in the polar regions or in the central Pacific where the air
turbidity can be extremely small and hence difficult to measure ac-
curately by using standard sun photometry techniques.
African Measurements
During the 1973 African solar eclipse expedition, one of the
authors (G.S.) made measurements of sky intensity from Loiyengalani,
Kenya (2°45'N, 36° 42'E, elevation 370m msl) on the southeast shores of
Lake Rudolf (Shaw, 1974). The aerosol optical depth on June 15, 1973 was
measured to be 0.155 at X = 500nm and 0.171 at A = 700nm. Large values
of T, such as the ones just stated were commonly observed at Loiyengalani.
Table 3 lists measured values from the period 6-13-73 to 6-30-73 at
500nm and 700nm.
53
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Table 3
Values of aerosol optical depth at Loiyengalani, Kenya
at wavelengths of 500 nm (Gn), and 700 nm (Rd).
Date
(1973)
6-13
6-14
6-15
6-16
6-17
6-18
6-19
1MV '
0.36
0.35
0.15
0.11
0.15
0.15
0.15
l|VjVJ/
-
-
0.17
0.175
0.195
0.19
0.20
Date
(1973)
6-20
6-22
6-24
6-25
6-27
6-30
Mv
0.225
0.15
0.17
0.095
0.040
0.29
Lf*/p '
0.25
0.20
0.22
0.16
0.095
0.17
As can be seen from Table 3, the aerosol optical depth in the red
(700nm) is generally larger than in the green (500nm). This anomalous
behavior is probably due to the fact that the African sub-Sahara aerosols
have many larger size particulates (r>l micron). This suggests that the
aerosols might originate from windblown dust which is probably carried
to great heights by convection. This surmise is strengthened by con-
current estimates of the horizontal visibility which were judged to be
generally better than one would expect considering the high optical
depths observed. Loiyengalani is located in an arid zone of East Africa
with a moisture index of approximately 55 (National Atlas of Kenya,
1970). The surrounding terrain is barren except for scattered patches
of bushed grassland. The ground albedo was measured photometrically in
the mid-visible; however, only half this value was used in the cal-
culations for the Rayleigh atmosphere to account for the low albedo over
the waters of Lake Rudolf.
54
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One can obtain a rough indication of the aerosol extinction scale
height, H., (the thickness that an aerosol layer would have if it were
distributed in a homogeneous layer with constant extinction coefficient
equal in magnitude to the appropriate ground-level volume extinction
coefficient) as follows: Horizontal visibility is defined as the dis-
tance where the constrast of a black-on-white target decreases to 2%.
This means that the horizontal transmission approaches a value of 0.02.
Assuming that Beer's law is valid, one can write T,, . . , = exp-(g R
+ BoM)L = 0.02 where BQR(A) is the molecular "Rayleigh" ground-level ex-
tinction coefficient and 3 .. is the ground-level aerosol coefficient, L
is the horizontal visibility, and T(x) the horizontal atmospheric
transmission. The equation implies that
L[3oM(A) + BoR(A)] = 3.9 18)
We note that the vertical aerosol optical depth, TM(A), may be derived
by measuring the apparent intensity of the sun. Furthermore, the values
of TM and TR can be set numerically equal to the product of the scale
height, H, and a ground level extinction coefficient BO(A) (i.e., TM(A)
= HM3 M and TR(A) = HRe R). By combining these expressions, one obtains,
H
nw
Thus by combining measurements of the horizontal visibility, L, with
measurements of the Mie optical depth, TM, one can derive a value for
the aerosol scale height, HL. Doing this for the measurements in Kenya,
we deduced that the aerosol scale height is of the order of 6 +_ 2km; about
3 to 4 times larger than values typically found in interior Alaska in
55
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spring. The larger values of hL in the tropics no doubt arise from a
combination of enhanced local convection and Hadley cell transport of
surface-generated aerosols.
Figures 17a through 17c show measurements of sky intensity in the
solar vertical and in the solar almucantar at A = 500 nm and A = 700 nm
at Loiyengalani. The scattering phase function deduced from these data
is illustrated (along with several other days' data) in Figure 18.
It is seen that considerable differences arise from one observation
period to the next. This, of course, reflects the fact that the physical
characteristics of the aerosols change with location, season, and synoptic
situation. Notice that the phase function curve derived on 15 June at
Loiyengalani, Kenya fits reasonably well to a Junge distribution (shown
as light lines in Figure 18) with a value of the exponent, v, equal to
2.5. This relatively small value of v is almost certainly associated
with the fact that the aerosols, in this particular instance, were
predominantly large, typical of what one might expect for windblown dust
(Joseph et_ al_., 1973). Comparison with the large value of v observed
during the forest fire episode (predominantly small particles) indi-
cates the usefulness of relating the measured aerosol scattering phase
function to the size distribution function. This shows that the aureole
method is useful in deriving information about origin of the aerosols.
Measurements on August 20, 1973
Figures 19a and b show curves of sky intensity measured on August
20, 1973, from Ester Dome, Alaska (64°53'N, 148°03'W). This was an
56
-------
0.50
i; 0.20
la
0,10
o>
c
0.05
0.02
SOLAR VERTICAL PLANE
15 June 1973
Loiyengalani , Kenya
X = 500 nm
=0.53
=0.155
-40 -20 0 20
Zenith Angle, Z
O
40 60
Figure ~\7a Sky intensity, Trl/Fo, in the solar vertical at Loiyen-
galani, A = 500nm.
57
-------
0.50
x
_ij
LL
w.
jg
£
M
o
0.20
0.10
o>
Q.
0.05
c
cu
0.01
T
T
SOLAR VERTICAL PLANE
15 June 1973
Loiyengalani , Kenya
X = 700 nm
ILQ =0.53
TM =0.171
tzenith
I
-60 -40 -20 0 +20 +40
Zenith Angle (Degrees)
+60
Figure 175 Same as above, except x = 700nm.
58
-------
X
CL
2.00
5 1-00
c/)
*4
O
? 0.50
0.20
(D
*C.
C/)
X
0.10
0.05
T
T
SOLAR ALMUCANTAR
15 June 1973
Loiyengalani, Kenya
X = 500 nm
fL0 = 0.52
TM = 0.155
1
0
20 40 60 80 100
Azimuth Angle (Degrees)
120
Figure 17c Sky intensity, nI/Fo, in the solar almucantar at
Loiyengalani, x = 500nm.
59
-------
100
50
CL
20
LL.
CD
(/>
o
ol
en
c
CD
D
O
10
O
(/)
O
t_
O)
0
15 June 1973
Loiyengalani .Kenya
20 August 1973
Ester Dome, Alaska
25 July 1973
College, Alaska
X = 500 nm
10 20 30 40
Scattering Angle (Degrees)
50
Figure 18 Aerosol scattering phase functions deduced from sky
brightness measurements.
60
-------
1.0
SOLAR ALMUCANTAR
0.1
(/)
CD
"c
Ester Dome , Alaska
20 August 1973
X0 =700nm
Mo =0-54
0.01
I
0
10 20 30 40 50
Azimuth From Sun (Degrees)
60
70
Figure 19a Sky intensity in the solar almucantar on August 20,
1973, A = 700nm.
61
-------
o
C\J
O
rO
O
CD
CD
CD O
Q ID
-CD
CP
< CD
c.
CD
N O
o
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o
o
O
O
tf>
o
o
C\J
a
o
o
lO
Q
0
O
o
CD
ID In
CD
o
CD
O
O
I/)
rs
CD
o
c:
«
'ca-
S-
cu
S-
rO
O
l/l
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jr
4J E
c
c o
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LO
i/i
l-O II
O)
c ^<
Jp
_c «
moo
r- l-~
5- cn
-Q i
O
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S-
CT)
u_
xny JDJOS ^0
AVJS x
62
-------
extremely clear period with excellent sky conditons with no trace of
striations. Horizontal visibility was estimated to be greater than 200
km since Mt. McKinley (distance 240 km) was easily visible with good
contrast.
The optical depth arising from scattering and absorption from
aerosols was so small on August 20th that it was extremely difficult to
determine its value accurately from sun-photometer data. Even with this
extremely minute aerosol optical depth, the effect of the atmospheric
aerosols on sky intensity is obvious in Figure 19. The dashed lines in
Figure 19 are calculated for an equivalent Rayleigh atmosphere having
T=TTotal Obs anc' t'ie Dotted line is for a pure Rayleigh atmsophere. The
utility of the aureole method for assessing aerosols becomes apparent
when one realizes that aerosol optical depths of these small magnitudes
cannot generally be determined accurately when they are deduced entirely
from sun-photometer methods.
Measurements on August 2, 1973
Figures 20a and b show diffuse sky intensity in the solar vertical
on August 2, 1973. The data were taken from the roof of the C.T. Elvey
building at the University of Alaska's Fairbanks campus. The optical
depths were TM(500nm) = 0.10, r..(700nm) = 0.069. Perturbation theory
analysis and comparison to pre-calculated curves of aerosol phase func-
tions indicate a value of \> of approximately 2.5 which seems to imply
large aerosols which may have originated at the surface and been carried
upwards by convection which was obviously taking place this day since
scattered cumulus were apparent along the horizon. (Incidently, the
63
-------
1.0
o
CO
^
LU
0.1
CO
I i I
SOLAR VERTICAL
2 AUGUST, 1973 a.m.
COLLEGE, ALASKA
X=500nm
60° 50° 40° 30°
ZENITH ANGLE
20C
10C
Figure 20a Sky intensity in the solar vertical plane on August
2, 1973, A = 500nm.
64
-------
1.0
n 1 1 r
O
C/)
^
LJ
0.1
SOLAR VERTICAL,
2 AUGUST, 1973 a.m.
COLLEGE, ALASKA
X=700nm
^0 = 0.69
r = 0.069
M
J I I I I I
J I
50C
40° 30° 20°
ZENITH ANGLE, Z
10C
0
Figure 20b Same as 20a, except for A = 700nm.
65
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analysis is probably not as accurate when there are scattered clouds
near the horizon, since their presence undoubtedly affects the sky
brightness; however, on this day the clouds were not extensive and were
mostly located close to the horizon, and therefore the error may not
have been large.) We remark that interior Alaska is extensively covered
by eolian loess (wind deposited glacial silt) which would add to the
large aerosol population under these conditions. Precipitation occurring
ten hours before the observations probably scavenged out small aerosol
particles in the air mass.
The unstable atmosphere, the extensive coverings of loess and the
previous rain washout, along with the small (v = 2.5) value of power-law
exponent all point to a mechanism of windblown fine dust carried upward
by convective currents as the responsible agent for introducing aerosols
into the air mass during this observation period.
The Effect of Cirrus Clouds on Sky Brightness
The presence of thin cirrus clouds modifies the sky radiation en-
vironment dramatically, especially at small scattering angles because of
diffraction of light around the ice crystals. To illustrate the effect,
we show, in Figure 21, the temporal variation of circumsolar sky in-
tensity as measured with the coronameter. Measurements are shown for
two wavelengths, 500 nm and 700 nm. At 12:50 LMT, a cirrus band of
approximate width equal to 15° was centered over the sun. This cirrus
band was caused from a jet contrail which had been seeded approximately
ten minutes earlier and which had spread out in a broad arc across the
sky. As time progressed, the cirrus band diffused out and eventually
evaporated. Figure 21 shows the attendant decrease of circumsolar sky
66
-------
100
50
C/)
o
i-
z>
CL
h-
Z>
o
20
10
0
Solar Almucantar,
Sept. 2, 1973 12'50AST
X=500nm
X=700nm
\
8 12
TIME (min)
16
20
Figure 21 Temporal variation of sky intensity centered on an
evaporating jet contrail.
67
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intensity with time. Unfortunately, the coronameter was not calibrated
and so the ordinate values can not be given in absolute units.
During the dissipation of the cirrus contrail, the Red/Green sky
intensity ratio decreased with time and this implies a change of scattering
particle size with time. Although these measurements are preliminary,
it appears that it may be feasible to use this method of sky photometry
to study the microdistribution of cloud particles.
Measurements^ on September 3, 1973
Figure 22 shows sky radiance at A = 500nm on September 3, 1973.
The solid lines refer to measurements made from Ester Dome (elevation
720m msl); the dashed line refers to measurements made from the Uni-
versity campus (elevation 213 m msl). Differences between the two can
mostly be attributed to aerosols contained in the height interval 213m
< h < 720m, (between Ester Dome and Fairbanks campus) although part of
the change is due to a slight solar elevation change. The dotted line
in Figure 22 indicates sky brightness for a pure Rayleigh atmosphere
with u =0.55. Although we have not done so, it is possible in this way
to determine size distribution data on atmospheric aerosols contained in
thin horizontal layers.
Aerosol Mass Loading
The mass of aerosols contained in a vertical column of air with
_p
unit cross-section, (g cm" ), may be calculated if one has knowledge of
the aerosol micro-distribution function (presumed not to vary with al-
titude) and the optical depth at one wavelength. Figure 23 shows the
volumetric aerosol extinction coefficient, B(500nm) calculated for an
assumed Junge power-law distribution function (Junge, 1963) with a
68
-------
1.00
1 r
0.50
SOLAR ALMUCANTAR,
3 SEPTEMBER, 1973
X^SOOnm
N
\
0.20
,^0.48 COLLEGE
0.10
= 0.55 ^-.^
ESTER DOMf"
0.05
r=0.145
RAYLEIGH
0.02
0
10° 20° 30°
AZIMUTH ANGLE,
40
50C
Figure 22 Sky intensity TrI/Fo, on September 3, 1973, in the solar
almucantar from Ester Dome, Alaska (solid) and from
College (dashed).
69
-------
3
constant volumetric mass-loading of 50 yg m and upper and lower cut-
off diameters of 10u and O.Oly, respectively. The abscissa is equal to
the Junge power-law exponent v. It can be seen that, for a constant
mass loading of aerosols, a power-law exponent numerically equal to 3.1
is most "efficient" for attenuating a light beam by scattering.
It is elementary to show that the following relation is true pro-
vided that the normalized size-distribution function is independent of
height:
r = (1 x 10"3) r(500nm) -^- (g m"2) 20)
2
where r is the aerosol columnar mass loading (g m~ ), T the aerosol
optical depth referred to the vertical, y = 50 ugrrf , and e is the
volume extinction coefficient (km~ ) calculated for y at the appro-
priate wavelength (Figure 23) and value of inferred Junge exponent v.
Using this technique we have calculated mass-loading values for
several clear days; the results are summarized in Table 4.
Table 4
Values of Columnar Aerosol Mass Loading, r
Date Location TM(500nm) v* r(g m"2)
15 June '73 northern Kenya .155 1.7 0.26
25 July '73 Fairbanks, Ak. .21 4.0 0.27
2 Aug '73 Fairbanks, Ak. .10 2.5 0.07
20 Aug '73 Ester Dome, Ak. .006 2.3 0.01
2 May '74 Fairbanks, Ak. .18 3.4 0.09
27 March '74 Barrow, Ak. .13 2.3 0.11
28 March '74 Barrow, Ak. .11 3.3 0.06+
30 March '74 Barrow, Ak. .13 3.2 0.06
31 March '74 Barrow, Ak. .13" 2.5 0.09
2 Apr '74 Fairbanks, Ak. .05 2.0 0.06
4 Apr '74 Fairbanks, Ak. .03 3.1 0.02
17 July '74 McKinley Park, Ak. .09 3.0 0.05
*v is the value of the estimated Junge power-law exponent.
70
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71
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Measurements in Arctic Alaska, March 25-31, 1974
Sky brightness and solar intensity were measured near Barrow,
Alaska at the NOAA background observatory (71°19'N, 156°37'W). The sky
was completely clear during the entire period March 26 to March 31;
winds were out of the northeast at approximately 8 msec" and the mean
day air temperatures were typically about -20 to -24°C. All local
sources of man-caused pollution (i.e., the village of Barrow and various
military radar stations) were downwind during the entire measurement
period. A rough trajectory analysis at the 700mb level indicates that
the air had passed almost directly over the North Pole and had veered
down over the northern extremities of the Canadian Arctic hence into
Barrow.
Unfortunately, the sky-brightness collimator photometer was not
available at Barrow. The sky intensity measurements were carried out
entirely with the coronameter at a mean wavelength of A = 550nm and mean
scattering angles of 1.10° and 6.2°. Optical depth, derived from sun
photometry, was measured at A = 500, 660, 700, 750, 850, 950, and 1,000
nni. In addition, although they will not be discussed here, vertical
profiles of aerosols were made with an airborne sun photometer. The
optical measurements were supplemented with acoustic sounder measure-
ments of the boundary layer which were being carried out at the time in
conjunction with the 1974 Lead experiment being conducted jointly by the
Universities of Oregon, Washington and Alaska. Also, in conjunction
with the "Lead experiment" ice crystals in the free atmosphere were
replicated and analyzed.
During the entire period mentioned above, one would expect, in view
of the conditions, that the air clarity would be excellent; there were
72
-------
no obvious sources of pollution or dust since the Arctic Ocean was
frozen and the surface was covered with a hard windblown snow pack.
However, visual observations indicated that there was a haze present in
the atmosphere. The horizontal visibility was estimated to be between
10 and 20 km, although this is difficult to reckon because of a lack of
reference points on the flat Arctic tundra. We did, however, attempt to
determine the horizontal visibility more accurately on one or two oc-
casions by making airborne observations. These involved flying at a
constant altitude of several hundred feet until a reference point, such
as a barrel or a caribou, appeared to "emerge" out of the haze; it was
then a simple matter of flying toward the object at a known airspeed and
measuring the time interval from "first sighting" until the airplane
passed directly over the object. Typically, the values of horizontal
visibility obtained in this fashion, varied between 10 to 20 km. In
addition to the low-lying haze near the surface, there were also indi-
cations that elevated haze layers existed at altitudes of one to two km.
Some of these layers appeared brownish-yellow probably reflecting the
fact that the aerosols in the haze layers had absorbtion features in the
visible region.
In addition to the multi-wavelength measurements of solar inten-
sity, we also carried out broadband measurements with a Linke-Feussner
Actinometer with OG1, RG2 and RG8 Schott-glass cut-off filters.
Generally speaking, the optical depths and circumsolar sky radiance
were large; much larger than one might expect for clear polar air.
Figure 24 shows values of optical depth arising from scattering and ab-
sorbtion by aerosols as a function of wavelength. Notice that the
optical depth at 950nm is anomalously large; this is due to the pax water
73
-------
0.5
0.3
0.2
0.1
0.06
0.04
3-28-74
3-30-74
3-31-74
pcrr
H20j
^
0.40
0.6
X (fJL)
0.8
1.0
Figure 24 Aerosol optical depth versus wavelength for 3 days in
March 1974, Barrow, Alaska.
74
-------
vapor absorption features. In principle, one can determine the pre-
cipitable water content in the atmosphere from the ratio T(950)/T(1000nm),
We are now calibrating this optical-hygrometer.
It is interesting and heartening to observe that the course of
optical depth with wavelength seems to obey a A~n type of dependency
which one would expect if the aerosols were distributed according to a
Junge power-law distribution over a sufficiently large range of particle
radii. Figure 25 shows the relation between the ratio of columnar mass
loading to aerosol optical depth, r/T.., as a function of wavelength A,
for a Junge power-law distribution. These curves were calculated using
the Mie theory, with an index of refraction = 1.54 + iO.O, and a mass
_3
loading of 50yg m . As can be seen from Figure 25, the Junge distri-
bution generally gives, at least approximately, (with the degree of
approximation depending slightly upon the choice of r, and r?) a A~n
dependency.
The circumsolar sky intensity was measured at Barrow with the sky
brightness coronameter at mean scattering angles of 1.1 and 6.2 . A
remarkably large variation occurred from day to day and even during
shorter time periods measured in minutes. Figure 26 is an example taken
from a chart record that shows the temporal variation in sky intensity
with time. The circumsolar sky intensity at a scattering angle of 1.1°
varied much more than at 6.2 .
We believe that the cause of the large sky intensity and atmo-
spheric extinction at Barrow is due primarily to the presence of ice
crystals which form at a high humidity region near the top of the mixing
layer. According to the acoustic sounder records, the mixing depth at
Barrow is approximately 200 meters thick. We found that there was a
75
-------
0.70
0. 10
0.4
O.5 0.6 0.7 0.8 0.9 1.0
Wavelength (X) in microns
Figure 25 Volume extinction coefficient versus wavelength
calculated for Junge size distribution function and
constant volumetric mass loading for various com-
binations of lower, r,, and upper, r^, cutoff radii.
76
-------
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77
-------
diurnal variation in mixing depth with larger (i.e. 250m) values found
during mid-day and smaller values (i.e., 150m) typically occuring at
night. From radiosonde data, and also from airborne temperature measure-
ments we found that the mixing layer is generally "capped" by an ele-
vated inversion with a strength of approximately 5°C. From the obser-
vations, it appears that the onset of ice crystal precipitations are
associated with the daytime expansion of the mixing layer, most likely
as the elevated inversion passes through humid layers to cause super
saturations. The radiosonde data often show a 100% humidity (with
respect to water) layer which is, we think, the responsible agent for
the ice-crystal precipitations.
In keeping with the aforementioned theory of ice-crystal formation,
we noticed that the ice crystal precipitation seems to start within an
hour or so from local noon; at that time, as the ice crystal concen-
tration increases, the sky intensity, especially near the sun (at 1.1°
scattering angle) increases manyfold. As an example of this we show in
Figure 27 a record of the sky intensity on March 26th. Coincident with
the high values at mid-morning, we observed optical effects including
circumzenith arcs, and 22° and 46° halos around the sun.
One would expect the diffraction of light around large (200y dia)
ice crystals to produce a strongly peaked phase function. The steepness
of the brightness gradient, 1(1.1°)/I(6.2°), of the circumsolar inten-
sity supports the assertion that there are large aerosols (ice crys-
tals) in the atmosphere. Thus it is quite clear that, at least on many
occasions, the ice crystals in the Arctic atmosphere are responsible for
78
-------
100
b 50
CO
-z.
LU
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10
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£ 1
MARCH 26, 1974
BARROW,NOAA
22°AND
44°HALO
CLEAR*
SKY
J I
I I
I I
09 10 11 12 13 14 15 16 17 18 19
TIME IN HOURS (LMT)
Figure 27
Diurnal variation of circumsolar sky intensity at
angular distances of 1.2 and 6.2° from the sun's
limb on March 26, 1974 at Barrow, Alaska.
79
-------
causing a large modification in sky intensity. Their presence almost
certainly cannot be neglected when assessing the heat budget of the
earth-atmosphere system.
In addition to the ice crystals, as we remarked earlier, there are
apparently some other types of aerosols present in the Arctic atmosphere
as evidenced from the yellowish streaks that were observed near the
horizon, from an altitude of one to two km, and also from the fact that
exposed mi Hi pore filters turned grey after passing air samples through
them. The aerosols were sampled with a flow-rate of 30 I/sec, an expo-
sure time of twenty-four hours, and a cross-sectional filter area of
2
10.0 cm . The pore size was 8y diameter. On every occasion, for a
total of six days, the filter collected enough aerosols to form a visible
film. Optical spectrophotometric measurements are presently being made
of the deposited aerosol film and preliminary results indicate that the
optical depth due to these aerosols is approximately 10% of the total
observed optical depth (at the mid-visible, A - 550nm). We tentatively
conclude that the ice crystals are primarily responsible for the ob-
served anomalies in circumsolar radiation and atmospheric extinction,
but, in addition, there may be another "chemical aerosol," possibly
nitrates for example, which may be present, and due to absorption, could
conceivably have an effect on the heat budget in the Arctic Basin. This
conclusion is surprising since the relevant air mass had had a long
trajectory extending for thousands of kilometers over frozen ice and
snow. Six days prior to our observation, according to a geostropic
trajectory analysis at the 700mb level, the air mass was in the vicinity
of northeast United States. It may be possible that the observed ab-
sorbing chemical aerosols had come from man-caused pollution.
80
-------
Measurements on May 2, 1974
We conclude our examples of sky brightness measurements with some
observations made on May 2, 1974, from the roof of the C.T. Elvey
building at the University of Alaska's Fairbanks campus. This example
is especially important for two reasons:
a) The sky was absolutely clear of clouds and no mottling or
inhomogenities could be seen; the sky appeared utterly homo-
geneous and dark blue, and
b) At the time of these measurements, the equipment which had
been under development during the course of this study was
reasonably complete and this was an excellent opportunity to
operate all of the instruments simultaneously so intercom-
parisons could be made.
Conditions were as follows: the winds were from the NE to E at
approximately 4 msec" ; snow had melted and the surface was approxi-
mately 80% exposed. During the entire period, there were no clouds.
The high sky purity was impressive.
Figure 28 illustrates the sky intensity in the solar almucantar
on May 2, 1974. The measurements were made with a well-baffled colli-
mator photometer up to 10 from the sun; triangles mark the coronameter
readings. Figure 29 shows the Langley plot of the direct sun radiation
and Figure 30 shows the wavelength dependence of the aerosol extinction
(optical depth). The aerosol source very likely resulted from surface
material mixed upward, or possibly advected in from the NE. Vegetation
was, for the most part dormant, and it is therefore unlikely that turpines
could have been a major contribution (Went, 1966) to the aerosol loading
for this particular period.
81
-------
2.00
ALMUCANTAR (/!=/£.)
MAY 2, 1974 p.m.
COLLEGE, ALASKA
1.00
Coronameter
data points
Whitish haze
o
0.50
CO
-z.
LaJ
0.20
0.10
0.05
0
T-0.35, A-0.25
T=145, A = 0.25
0
30° 60° 90°
-AZIMUTH ANGLE
120C
Figure 28
Sky intensity, irl/Fo, in the solar almucantar on May
2, 1974, A = BOOnm, College, Alaska.
82
-------
Ld
O
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r>
Q_
I
Z)
O
(T
LJ
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Q_
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0.1
LANGLEY PLOT
MAY 2, 1974 p.m.
COLLEGE, ALASKA
VIS120km
Intercept Values Determined
From Std. Lamp Calibration
a
A
450nm
850nm
950nm
lOOOnm
TT =0.107
r = 0.201
TT =0.080
0
234
AIR MASS - m(Zo)
7
Figure 29 Langley plot of direct-sun data on May 2, 1974 at
College, Alaska.
oo
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-------
0.50
0.40
.20.30
l-
LuO.20
o
h-
Q_
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_,
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0.15
0.10
§0.07
0.05
0.03
MAY 2, 1974
COLLEGE, ALASKA
= 0.071, a
-a
0
H20 Abs.
yOCTT
Band
300 400 600 800 1000 1500
WAVELENGTH (nm)
Figure 30 Wavelength dependency of aerosol optical depth on May
2, 1974 at College, Alaska.
84
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THE RELATION BETWEEN THE JUNGE POWER-LAW EXPONENT
AND THE AUREOLE BRIGHTNESS GRADIENT
As has been mentioned previously, suspended aerosols in the atmo-
sphere strongly diffract light into the near forward directions. At
least for the larger aerosols (r>ly), the distribution of scattered
energy is in rough accord with results predicted by classical Fraun-
hofer diffraction theory. That is, the angular extent of the primary
diffracted energy increases as the scattering particle size decreases.
Therefore, small scatterers will yield a relatively large aureole while
larger aerosols will diffract energy into a relatively smaller core. If
size distribution of aerosols were mono-disperse, one would observe
colored diffraction rings around the sun; however, this usually does not
happen in practice because of coagulation resulting from Brownian motion
and precipitation due to gravity acting together to yield a broad aerosol
spectrum covering a wide range of particle radii. Theoretical analysis
by Freidlander (1961) shows that a power-law distribution function of a
form suggested by Junge, would result in a steady-state situation of
coagulation-gravitational fallout.
In view of what has just been said, we see that the hypothetical
"diffraction pattern" formed by a mono-disperse distribution of parti-
culates in the atmosphere would be blurred and one would expect instead
to find a diffuse whitish glow around the sun superimposed on the blue
sky, and this is exactly in accord with what one generally observes
(except in special rare cases, Deirmendjian, 1971). However, from the
arguments just presented, the intensity gradient close to the sun will
depend on the steepness of the aerosol size distribution function. All
85
-------
other factors being equal, a rapidly falling spectrum (large power-law
exponent, v) will have relatively more small particles per unit volume
than a size distribution with a more gradual fall-off of number con-
centration with increasing radii (small value of v). We conclude that
large values of v will be associated with a larger, more homogeneous
aureole than the converse.
Numerical modeling using Mie theory to generate aerosol scattering
phase functions, P(e), for the Junge size distribution with different
values of v shows that this is indeed the case. Figure 31 illustrates
the intensity gradient, 1(1,2°)/1(6.5°), as a function of the Junge
power-law exponent, v. We see that the ratio approaches unity for large
values of v, which indicates that, at least within an angular distance
less than 6.5 from the sun, the aureole would be homogeneous and flat
(lacking a brightness gradient) if v were numerically equal to 4.0. On
the other hand, a small value of v, say v = 2.5 as we find to be typical
for windblown dust, gives a strongly peaked brightness gradient with a
ratio of 1(1.2°)/I(6.5°) equal to about 4.
To eliminate the effects of molecular scattering, one must first
subtract out the Rayleigh "blue sky" from the observations and use the
subtracted intensity values. These values are designated with a sub-
script "M" in Figure 31, and they more closely resemble the brightness
gradient for the aerosol component alone.
Assuming that a Junge power law distribution adequately describes
the aerosol spectrum, then the exponent value, v, can simply be de-
termined from the ratio of the coronameter's readings by using the curve
in Figure 31. Conversely, if one begins with a size spectrum such as
86
-------
7
JOBS (1.2°)-lRAY( 1.2°)
IOBS(6.5°)-lRAY(6.50)
o
CO
o
in
CD
0
2.0
Figure 31
3.0 4.0
JUNGE EXPONENT,v
Ratio of sky intensity at 1.2° and 6.2° as a function
ot the Junge power-law exponent,
V.
37
-------
that given by Deirmendjian as HAZE M, the brightness gradient can be
found on the ordinate opposite the appropriate point on the curve in
Figure 31. Of course, to be more accurate and quantitative, one should
evaluate (by using the method that we have described) the aerosol scat-
tering phase function out to 30 or 40 degrees and relate the curve to a
size distribution function by either a formal inversion process or by
using a curve-matching technique. As we have pointed out before, how-
ever, the accuracies with which one can actually determine the phase
function is limited by a combination of such things as uncertainities in
surface albedo, instrument absolute calibration, inherent difficulties
in the perturbation approximations, etc. We feel, after having taken
much data and worked with the numbers, that one can probably not use the
photometer measurements of the aureole to derive extremely fine struc-
ture in the size distribution function, and, again, we find that a
simple function such as the Junge power-law distribution or the modified
gamma function can be made to fit by choosing various parameters within
the limits of the uncertainties.
In summary, a Junge size distribution seems to be a reasonable
first choice when attempting to match sky brightness data with cal-
culated curves. Usually the results are quite consistent (at least for
continental aerosols, the only ones which we have studied), and the
aureole brightness gradient, 1(1.2°)/I(6.5°), provides a simple means
for estimating a quantitative index (value of v) of the aerosol size
distribution.
88
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References
Allen, C. W., Astrophysical Quantities, 2nd Ed., University of London,
The Athlone Press, London, 1963.
Bullrich, K., "Scattered radiation in the atmosphere," Advances in Geo-
physics, 10, Academic Press, N.Y., 1964.
Chandrasekhar, S., Radiative Transfer, New York, Dover Publications,
393 pages, 1950.
Coulson, K. L., J. V. Dave, and Z. Sekera, Tables Related to Radiation
Emerging from a Planetary Atmosphere with Rayleigh Scattering,
Berkeley and Los Angeles, Univ. of California Press, 548 pages, 1960.
deBary, E., B. Braum, and K. Bullrich, Tables related to light scattering
in a Turbid Atmosphere, Vol. 1, 2 and 3, Air Force Cambridge Research
Laboratory Report, AFCRL-65-710, 1965.
Deirmendjian, D., Electromagnetic Scattering on Spherical Polydispersions,
American Elsevier, New York, 1969.
Deirmendjian, D., Use of Scattering Techniques in Cloud Microphysics Research
1. the Aureole Method., RAND report R-590-PR, October 1970.
Diermendjian, D., Global Turbidity studies I, RAND Report R-886-ARPA,
October 1971.
Eddy, J. A., The stratospheric solar aureole, Ph.D. Dissertation, University
of Colorado, Boulder, Colorado, 1961.
Eiden, R., Calculations and Measurements of the Spectral Radiance of the
Solar Aureole, Tellus XX, p. 380, 1968.
Elsasser, H., The Zodiacal Light, Ha net. Space Science, 11, 1015-1033,
1963.
Elterman, L., UV, Visible and IR Attenuation for Altitudes to 50km, 1968,
AFCRL Report No. 68-0153, Environmental Research Paper No. 285,
Bedford, Massachusetts, April 1968.
Evans, J. W., A Photometer for Measurement of Sky Brightness Near the Sun,
JOSA, 38^, #12, 1083, 1948.
Fletcher, J. 0., The Heat Budget of the Arctic Basin and its Relation to
Climate, United States Air Force Project RAND Report R-444-PR,
October 1965.
Freidlander, Theoretical considerations for the Particle size spectrum of
the Stratospheric Aerosol, J. of Meteor., 18, 753, 1961.
89
-------
Green, A., A. Deepak and B. Lipofsky, Interpretation of the Sun's Aureole
Based on Atmospheric aerosol models, Applied Optics, 10, No. 6, 1263,
June 1971.
Herman, B. M., S. R. Browning and R. J. Curran, The Effect of Atmospheric
Aerosols on Scattered Sunlight, J. Atmos. Sci., 28, No. 3, 419-428,
April 1971. ~ ~
Joseph, J. H., A. Manes and D. Ashbel, Desert aerosols transported by
Khamsimic depressions and their climatic effects, J_. Applied
Meteor., 12, 792-797, 1973.
Junge, C. E., Air Chemistry and Radioactivity, Academic Press, New York,
382 pages, International Geophysical Series-Volume 4, 1963.
Kasten, F., A new table and approximate formula for the relative optical
air mass, Tech. Dept. 136, CRREL, AD610554, 1964.
Lloyd, J. W. F. and S. M. Silverman, Measurements of the Zenith Sky In-
tensity and Spectral Distribution during the Solar Eclipse of 12
November 1966 at Bage, Brazil, and on an Aircraft, Applied Optics,
JO, No. 6, 1220, June 1971.
Mie, G., Beitrage zur Optik Truber Medien, Annalen der Physik, 25, January
1908.
Mitchell, J. M., Jr., The Effect of Atmospheric Aerosols on Climate with
Special Reference to Temperature Near the Earth's Surface, Journal
of Applied Meteorology, 16, 703, 1971.
Rasool, S. I. and S. H. Schneider, Atmospheric Carbon Dioxide and Aerosols
Effects of Large increases on Global Climate, Science, 173, 138-141,
9 July 1971.
Shaw, G. E., Sky brightness and polarization during the 1973 African eclipse,
Appl. Optics, February 1975.
Stair, R., W. E. Schneider and J. K. Jackson, A new standard of spectral
irradiance, Applied Optics, 2, No. 11, 1151-1154, 1963.
Thekaekara, M. P., Solar irradiance measurements from a research aircraft
at 38,000 feet, Report X-322-66-304 (Goddard Space Flight Center,
Greenbelt, Maryland) August 1968.
Van de Hulst, H. C., Light Scattering by Small Particles, John Wiley and
Sons, New York, 1957.
Went, F. W. , On the nature of Aitken condensation nuclei, Tellus^ 18, 549-
556, 1966.
90
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APPENDIX A. UNITS OF SKY BRIGHTNESS
Units of Sky Brightness
Diffuse intensity is expressed in a bewildering array of units.
Each discipline (astronomy, aeronomy, meteorology, etc.) seems to have
its preferred system. For the benefit of the reader who may want to
express intensity measurements in other units, we present a discussion
of the commonly used units and the relation among them.
a ) Physical units of absolute intensity, I (x), (commonly expressed
-2-1 -1 2 -1 " -1
in MW cm nm sr , identical to erg cm" sec A ).
The power passing through an aperture of a photometer, p(x),
having a circular field of view of angular diameter, e, is,
p(\) = I (\) dA dw d\ Al)
2
where, for example, p is the radiant power in microwatts, dA is in cm ,
2
du)=Tte /4 (e measured in radians), and dA is a wavelength interval in nm.
b) Sky intensity expressed in units of mean sun brightness, B(A).
Solar astronomers often express sky intensity in "millionths of
the sun's brightness." The following expression defines B(x):
B(\) = I(\) A2)
p
-2 -1 -1
where I is expressed in pw, cm nm sr then F , the extraterrestrial
2 -1
solar flux, would have to be in \\\n cm nm . dw is the solid angle of
_c
the sun as viewed from earth, (dw = 5.95 x 10 sr). It should be re-
membered when using intensity expressed in units of mean sun brightness,
that the values are referenced to the extraterrestrial value of solar
flux and not to the observed ground-level solar flux which is smaller
due to atmospheric extinction.
91
-------
c) Sky intensity expressed in rayleighs/angstrom, R".
This unit is in common usage among researchers in aeronomy as a
means of expressing the volume emission of the airglow integrated along
the line of sight as equivalent to a surface brightness. To prevent
confusion one should remember that there are two distinct situations:
1) expressions for the total intensity of an individual spectral line
(such as the forbidden atomic oxygen line at 5577A). In this case, the
brightness is expressed in "rayleighs," R. 2) expressions for the
brightness of an extended source with a continuum-type of spectrum. An
example is the non-resonant scattered sunlight in the atmosphere. In
this case one must express the intensity in per-unit wavelength interval
(rayleighs per angstrom, R').
The intensity of an extended object (not a point object) in rayleighs/
A is defined as:
*- ^ - ^x io~6 - A3>
where n = photon flux entering the photometer aperture (sec~ )
dui = solid angle of the photometer's field of view (sr)
2
dA = entrance aperture in cm
dA = wavelength width in A
The photon number density, n, (sec~ ) is given by,
n = "He" A4^
where A is the wavelength (m)
p the incoming power (watts)
h = Plancks constant = 6.624 x 10 joule-sec
c = speed of light = 3.00 x 108 (m/s)
for mid-visible light at a wavelength of 550 nm, n = 2.76 x 1018p
(sec"1
92
-------
Equation Al, A2, and A3 can be combined to yield a convenient
21-1
relation between intensity I (A) in (yw cm" nm~ sr~ ) and R"(A) (ray-
lei ghs/A):
R'(A) = 6.32 x 106AI (A) A5)
where Am = mean wavelength in ytn.
d) Stellar magnitude, m
Stellar magnitudes are used by astronomers to express radiant flux
(not intensity). They are commonly used to express the brightness of
stars. The absolute stellar magnitude, m , is related to absolute in-
coming flux F(A) by,
log1Q F(A) = 0.40mv - 8.42 A6)
? -l
where F is in (yw cm" nm~ ).
e) Chandrasekhar's convention forradiant flux
The definition of radiant flux, F , as given by Chandrasekhar
L*
(1950) incorporates a factor of TT which in the past has caused some
confusion. A case in point is the somewhat common practice of expres-
sing intensity in units of incoming flux. For example, in the well-
known tables of Coulson _e_t aj_., are listed solutions to the equations of
transfer for Rayleigh scattering atmospheres, and the intensity values
are expressed in units of incoming flux, assuming a radiant flux which
has incorporated the value of i\ in its definition. In using such
numerical tables, one must use care in the interpretation of the values.
Flux, as defined by Chandrasekhar, is,
FC(A) = | f I(A) cosedu) A7)
which has the advantage of yielding F = I for an isotropic radiation
field.
93
-------
On the other hand, in solar radiation work it is common to drop the
factor of TT and to express the solar flux, instead, as simply:
FQ(A) - f I(A) cos(e) dw A8)
wi
where the integral extends over the solar disk. This is the definition
that was used for flux in part b) of this section.
Thus, if one uses the tables of Coulson ej^ a]_., the sky intensity,
I(A), is related to the tabulated values, TV , as follows,
TV^TIT" A9>
0
In DeBary j^t aj_. 's tables (1965), the tabulated values of diffuse sky
-2 -1 -1 ' -1
intensity are expressed directly in units of cal cm" min" sr~ (100A)"
assuming that the extraterrestrial flux is given by the Tables of Nicolet
(1951).
f) Numerical examples of diffuse intensities and direct fluxes
for various sources.
It is perhaps useful to present a table giving the intensity of
various natural objects in terms of the above definitions so that the
the numbers can be compared, and so one can obtain a more quantitative
"feeling" for the brightness of natural objects. Table Al lists the
intensities and fluxes for commonly observed sources of interest. One
should realize that in some cases, the actual brightness of objects
varies depending upon conditions.
94
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APPENDIX B
COMPUTATION OF GEOMETRICAL PARAMETERS
A. The Solar Zenith Angle
The zenith angle of the sun, z, is computed by solving the celestial
triangle. In terms of terrestrial coordinates, it may be expressed as,
cos(z) = sin £ sin 6 + cos £ cos 6 cos H Bl
where £ = observer's latitude
6 - solar declination at time of observation
H = solar hour angle measured westward from the southern meridian.
The sun's hour angle, H, is computed according to the formula,
H - LST + SLD - LLD - E + 12 hr. B2
where the symbols refer to times units as follows:
1ST is the Local Standard Time of the observation,
SLD is the standard time zone difference, in hours, to the prime
meridian;
LLD is the longitude of the observation site in units of time
15° per hour of time); and
E is the equation of time.
One may determine E for the time and date of observation from an
ephemeris tabulation, or it can be calculated by using:
E = 2e sin(l -w) - tan(|)2 sin(2 1 ) B3
where e - eccentricity of earth's orbit
1 = longitude of sun,
w = longitude of sun's perigee,
C = obliquity of the ecliptic.
97
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The terms e, w and C can be taken from an ephemeris for any given
year. Equation B3 has the advantage that it may be used to make cal-
culations for multiple periods in any given year thereby saving looking
up E for each observation period which can become inconvenient if large
numbers of observation dates are to be calculated.
The solar longitude, 1 , is measured along the ecliptic from the
first point of Aries, It can be easily computed from
10 = (Deqn - DQbs) 360/365.25 degrees B4
where D and D , represent the dates (in decimal days from an arbi-
eqn obs
trary reference point, say January 1 at 00 hours) for the local equinox
and the observation date respectively.
B. The Air Mass, m(z).
The solar air mass, m(z), represents the amount of absorbing/scat-
tering medium, in a unit cross-sectional area, through which an incoming
ray from the solar disk passes. It is measured in units of absorbing/
scattering material for a ray entering from the local zenith direction.
For relatively large solar elevation angles, the air mass can be derived
to a high degree of approximation by considering the atmosphere to be a
horizontally homogeneous plane parallel layer. For such a model, the
air mass is simply given as,
m - sec(z) B5
When the sun's elevation angle becomes small, the curvature of the atmo-
sphere can no longer be neglected and the sec(z) expression becomes
progressively more inaccurate. In instances of low sun angle, the air
mass must be calculated by integrating along the absorption and scat-
tering medium encountered by a ray bundle of incoming solar rays con-
98
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tained in a unit area and passing through the atmosphere. Refraction of
the incoming ray by the varying atmospheric density with height must be
included in the computation, particularly for solar elevation angles of
a few degrees. One finds, by analysis, that the magnitude of the air
mass, for low sun angles, becomes dependent on the nature of the verti-
cal distribution of aerosols and gaseous molecules. Tables have been
constructed by several investigators for various kinds of model atmo-
spheres giving the air mass as a function of "apparent" zenith angle.
We used the tables prepared by Kasten (1964) which list the air mass
function for an ARDC model atmosphere.
The air mass values tabulated by Kasten were fitted to an empirical
expression of the form,
m(e) - B6
sin e + a(e + b)~
Kasten gives the following values for the constants in equation B6: a
= 0.1500, b = 3.885, c = 1.253.
The formula B6 fits the computed data points to an accuracy of
better than 1.5% over the entire range of elevation angles from zero to
90°. For most zenith angles the accuracy is considerably better, on the
order of a few tenths of one percent, completely adequate for most
radiation transfer purposes.
C. Scattering Angle, e.
The scattering angle, e, is measured along a great circle arc from
the direction specified by a zenith angle, z, and an azimuth angle, ,
and the direction of the sun specified by corresponding coordinates zn
and ({>; it may be expressed as,
99
-------
^nf.r0\ - x / - o - o~ cos(e-en), B7
cos(e) - py0+ /(1_yo2)(1_y2) 0''
where u and yQ refer to the cosine of Z and Zn.
D. Effects of Altitude, h.
The air mass, m(z), is, as was explained above, referred to the
amount of absorbing and scattering media in a vertical column above
the observer. One should recall, however, that the absolute amount of
material, and hence the extinction coefficient, depends on the obser-
ver's elevation above sea level. The effect of elevation change can be
related to change in the total vertical optical depth by accounting for
the pressure change. Therefore, if one has available tables of optical
depth arising from Rayleigh on molecular scattering, TD(A), evaluated
K
for STP, then one may estimate the pressure-corrected optical depth by
scaling according to
. B8
P0
where p(h) and p(0) are atomspheric pressure at height h and at sea
level. For most purposes one may obtain p(h) from a standard atmosphere
model .
100
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TECHNICAL REPORT DATA
(Ttoiir rtad Instructions on the reverse before completing)
T
1. REPORT NO,
EPA-650/4-75-OT2
RECIPIENT'S ACCESSION>NO.
4. TITLE AND SUBTITLE
RELATIONSHIP BETWEEN CIRCUMSOLAR SKY BRIGHTNESS
AND ATMOSPHERIC AEROSOLS
i. REPORT DATE
June 1974
I. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Glenn E.
Shaw and Charles S. Deehr
I. PERFORMING ORGANIZATION REPORT NO.
0. PERFORMING ORGANIZATION NAME AND ADDRESS
Geophysical Institute
University of Alaska
Flarbanks, Alaska 99701
10. PROGRAM ELEMENT NO.
1AA009 ROAP No. 26AAS
11. CONTRACT/GRANT NO.
801113
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency-NERC
Meteorology Laboratory (MD-80)
Research Triangle Park, N. C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final Report 9/72-6/74
14. SPONSORING AGENCY CODE
16. SUPPLEMENTARY NOTES
16. ABSTRACT
Measurements of the sky intensity in the solar vertical plane and in the solar
almucantar were taken at an arctic location near Barrow, Alaska (71°19'N, 156°37'W),
a sub-arctic location at Ester Dome, Alaska C64°53'N, 148°03'W), and a tropical
station at Loiyengalani, Kenya (2°45'N,36042'E)t The data were used to obtain the
aerosol scattering phase function for various synoptic conditions and air-mass
types. The scattering phase functions were compared to calculated phase functions
obtained by assuming various, forms of the aerosol size distribution function. Based
on the criteria of the best fit of the phase functions the corresponding aerosol
size distribution function and the quasi-monochromatic optical depth, numerical
estimates were made of the columnar aerosol mass loading. Typical of continental
observations, a Ounge power-law aerosol size distribution approximates the observed
scattering phase function rather well. The observations indicate that the Junge
power-law exponent, v, depends upon air mass type and to a lesser extent on local
climatological conditions. Relatively large values for the exponent (v = 4.0) were
obtained for aerosols due to smoke from a forest fire in Siberia. Smaller values
of the exponent (v = 2.5 to 3.0) were obtained for clear conditions in an unstable
convectlng atmosphere.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Sky Brigthness
Particle size distribution
3, DISTRIBUTION STATEMENT
Release Unlimited
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Relation between sky
brightness and atmospheri
aerosol distributions
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (Tins page)
Unclassified
21. NO. OF PAGES
113
22. PRICE
EPA Form 22JO-! (S-73)
101
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