AFCRL-68-0153: APRIL 1968
ENVIRONMENTAL RESEARCH PAPERS, NO. 285
AIR FORCE CAMBRIDGE RESEARCH LABORATORIES
L. H.ANSCOM FIELD, BEDFORD, MASSACHUSETTS
UV, Visible, and IR Attenuationfor Altitudes to 50 km, 1968L. ELTERMAN
OFFICE OF AEROSPACE RESEARCH
United States Air Force
-$7
AFCRL.68-0153APRIL 1968ENVIRONMENTAL RESEARCH PAPERS, NO. 285
OPTICAL PHYSICS LABORATORY PROJECT 7670
AIR FORCE CAMBRIDGE RESEARCH LABORATORIESL. 0. HANSCOM FIELD, BEDFORD, MASSACHUSETTS
I r
UV, Visible, and IR Attenuationfor Altitudes to 50 km, 1968L. ELTERMAN
Distribution of this document is unlimited. It maybi released to the Clearinghouse, Department ofCommerce, for sole to the general public.
OFFICE OF AEROSPACE RESEARCHUnited States Air Force
VIP
[i
Abstract
An atmospheric attenuation model for the ultraviolet, visible,. and infraredI
was developed in 1964, based on scattering (molecules and aerosols) and ozone ab-
sorrtion. Since then more measurements have been made and our knowledge of
aerosol attenuation has widened. These circumstances result in attenuation model
changes which are relatively unimportant for most exploratory calculations. They
can be significant, however, for long slant-path high-altitude applications entailinglarge zenith angles, factors which characterize, for example, the measurement
geometries of rockets and satellites. Accordingly, a revision of the 1964 Attenua-
tion Model is warranted.
In this paper the optical parameters are computed spectrally and with altitude
as follows: (1) pure air attenuation parameters are determined by utilizing ýayleighscattering cross sections with molecular number densities from the standard at-
mosphere; (2) ozone absorption parameters are derived based on Vigroux's coeffi-
cients applied to a representative atmospheric ozone distribution; (3) seven sets
of aerosol measurements are compared and a profile of aerosol attenuation coeffi-
cients vs altitude is developed. Attenuation coefficients and optical thickness due
to molecular, aerosol, and ozone attenuation are computed and tabulated individual-
ly so that the influence of each can be compared. The newly derived tabulations
permit various exploratory calculations, including horizontal, vertical, and slant-
path transmission at kilometer intervals to an altitude of 50 km, individually for
each attenuating component or for overall atmospheric extinction (molecular +
ozone + aerosol).
iii ,
I
IJ
Contents
1. INTRODUCTION 1
2. RAYLEIGH PARAMETERS 3
3. ABSORPTION PARAMETERS FOR ATMOSPHERIC OZONE 7
44. AEROSOL ATTENUATION 8
5. ATMOSPHERIC EXTINCTION 20
6. 'EXPLORATORY TRANSMISSION CALCULATIONS 20
7. CONCLUDING REMARKS 21
8. TABULATION OiF PARAMETERS 21
ACKNOWLEDGMENTS 45
RE.FERýNCES 47
Illustrations
1. Index of Refraction for 1013 mb and 151C (Table 1) 4
2. Rayleigh Cross Section vs Wavelength (Table 1) 43. Representative Atmospheric Ozone Concentration l'rofil,2 (Table 2) 74. Aerosol Attenuation Coefficients vs Altitude at = 0. 55p 9
Illustrations ; /
5. Single Profile I3u(h, AI) for 11 April 1964 ft 02:00 MST, Similar toMean of 79 Pofiles 1i
6. Single Turbidity Profile A3p(h, X )/Pr(h, A) for 11 April at 02;00 MST 12
7. Mean of 79 Low Stratospheric Dust Profiles (Table 3) forApril 1964 to April 1965 14
8. Mean Turbidity Profile #3p(h,..X1)/5r(h, '1) 15
9. Expanded Scale for 26 to,32 km Altitude Region Showing Hp 3.75 kmfor 79 Profile Mean p 16
10. Comparison of Profiles 1711. Aerosol Attenuation Coefficients pp(O, X) vs Wavelength at Sea Level
for a Meteorological Range Approximating 25 km 19
Tables
1. Model Parameters as a Function of Wavelength 2
2. Model Parameters as a Function of Altitude 63. Aerosol Optical Thickness as a Measure of Volcanic Dust, X = 0. 55gi 13
4. Parameters at 0.27p to 4 . 00 (Tables 4. 1 to 4.22)
vi
-iA
I /
S~Symbols
A. Vigroux ozone absorption coefficient (cmat ) S bD Ozone concentration (cm/kin)
d Horizontal path length (kin) pH Aerosol scale height (kin)
ph Altitude (km)
K Mie scattering efficiency
m Aerosol index of refraction
m Index of refraction at sea level, air at 1013 mb and 150C
N3 Ozone number density (cn 3 )3-
N Aerosol number density (cm
N Molecular number density (cm 3 )
N Molecular number density at sea level (cma")
r Particle radius (microns)
t Turbidity (3prT Temperature °K
Th Horizontal transmission
T0h Transmission between sea level and altitude h
Th-.v Transmission between h and space
T Ah Transmission between two altitudes above sea level
13~ Atmospheric ozone absorption coefficient (kmi)
1p Aerosol attenuation coefficient (kin1 )
(h, X)Mean of 79 profiles for X 0.55 microns (kW")
vii
-',
O•r Rayleigh attenuation coefficient (kmn
""3ext Extinction coefficient (kmi) ¶
•"I L)epolarization factor
!. Zenith angle
Wsvelength (microns or cm)Wavelength 0. 55 microns
ar Rayleigh scattering cross section (cm 2)
r3 Ozone optical thickness from sea level to altitude h (0-h)Ozone optical thickness from altitude h to space (h-,) Y'
T Aerosol optical thickness from sea level to altitude h, (0-h)pC Aerosol optical thickness from altitude h to -pace, (h-o)-p
r Rayleigh optical thickness from sea level to altitude h, (0-h)
r Rayleigh optical thickness from altitude h to space, (h-') IS~r~ext Extinction optical thickness (molecular + ozone + aerosol)ext from sea level to altitude h, (0-h)
7t Extinction optical thickness (molecular + ozone + aerosol)from altitude h to infinity, (h-m<.1
Aerosol size distribution function
Vl
viii 4
S,?
UV, Visible, and IR Attenuation for Altitudes to50 kmn, 1969"
I. INTROIDIUCTION
In 1964, an atmospheric attenuation model was published (Elterman, 1964)
which has'been useful for a variety of exploratory calculations. Now a revision is
warranted for reasons given in the abstract and Section 4 of this report. In this
revision most of the earlier material is presented in summary form. The section
on attenuation by Rayleigh scattering, however, is retained because the content
leading to the derivation of the Rayleigh parameters is useful. In one instance,
due to existing interest, the material is expanded, i.e. , the tabulations which com-
prise the attenuation model now include aerosol and ozone optical thickness so that
a comparison can be made of the relative importance of each attenuating component
for vertical and slant paths.
The shortest wavelength considered is 0.27 microns. The use of shorter wave-
lengths would require a treatment of 01, absorption. Also, attenuation is suffi-
ciently severe so that interest in the shorter wavelength region for purposes of
ultraviolet transmission below 50 km probably is limited. The longest waivelength
used is 4.0 microns. Calculations for longer wavelengths are complicated hv the
presence of absorption bands of I110, CO),,, and their wings. In between, n total
of 22 wavelengths is chosen (Table 1) within the atmospheric windows and for the
ultraviolet region where ozone absorption is important.
(1leceived for publication 25 March 1 )(I)
2
Conceptually, the attenuation model starts with moleculardensities from thelatest published U.S. Standard Atmosphere (1962) followed by the addition of ozone
and aerosol components. The meteorological range (M.R.) at sea level correspondsto about 25 km at 0. 5 5p wavelength. This choice serves a useful function because
it permits including some important measurements conducted at X - 0. 550 . Inaddition, this wavelength customarily represents the phototopic region.
Table 1. Model Parameters as a Function of Wavelength
A (microns) m5 a or (cm 2) A (cm"I)26 2
0.27 1.00029668 8,960 X to-26 2.IOX 10 20.28 1.00029475 7.646 X 10- 1.06X 1020.30 1.00029156 5.677X 10- 1.01 X 101
-260.32 1.00028902 4.310X 10 2 6 8.93X 100.34 1.00028699 3.334 X 10 26 6.40x Xo2 I I0.36 1.00028531 2.622X 10 26 1.8ox 10o3
0.38 1.00028392 2.091 X 10-26 00.40 1.00028275 1.689 X -26 00.45 1,00028052 1.038 X to26 3,50X 10-
0.50 1.00027896 6.735X 0-27 3.45X 1o 2
0.55 1.00027782 4.563X 0-27 9.20X to20.60 1.00027697 3.202 X 10 27 1.32 X 1010.65 1.0002763.0 2.314 X 10 2 7 6.20X 102
0.70 1.00027518 1.714 X 10" 27 2.30X 10'2
0.80 1.00027503 9.990 X 10- 2 8 1.00 X 10- 2
0.90 1.00027451 6.213 X 10 2 0
1.06 1,00027397 3.216 X 10- 2 8 01.26 1.00027357 1.606 X 10- 28 0
1.67 1.00027315 5.189 X 10"2 9 0
2.17 1.00027292 1.817X -29 03.50 1,00027272 2.681 X 10-30 04.00 1.00027269 1.571 X 10- 0 0
- Wavelength
ms - Index of refraction (1013 mb, 15°C)
or - Rayleigh scattering cross sectionAbsorption coefficient after Vigroux for pure 03., smoothed
v values (1013 mb, 18*C)
4AI
3
2. RAYLEIGH PARAMETERS
A fundamental requirement for generating an accurate series of Rayleigh
parameters is an exact dctcrmination of the index of refraction for the wavelengths
of interest. With this known, the Rayleigh cross sections can be computed. This
in turn permits computation of the Rayleigh attenuation coefficient and its variation
with altitude as well as corresponding optical thickness values.
The index of refraction for a standard atmosphere (1013 mhb, 15°C) specifically
for the desired wavelengths used is determined by Edlen's (1953) expression
(ma 1)10~ .- 6432.8 + 2949810 25540146 - 0)7) 41 - -2)
where m. = refractive index
X - wavelength (microns)
Penndorf's (1957) computations using Eq. (1) demonstrate that the effect of water
'vapor can be neglected and'the derived m 'values have negligible error for the
spectral range from 0. 2 to 20.0 microns.
The R•ayleigh cross section is expressed by
3 - (2)
where
r ' the Rayleigh scattering cross section (cm 2 ),Sthe wavelength (cm),
'Me a the index of refraction of air at 15C and 1013 mb pressure,
N a the molecular number density at sea level for a standardatmosphere (cm- 3 ),
6 a the depolarization factor.
The term (6 + 36)/(6 - 78) accounts for the degree of depolarization attributable to
the anisotropy ofthe atmospheric moleculb,. The depolarization factor has been
determined by-calculation and by laboratory measurement. The latest work of
Gucker and Basu (1D53) yields 6 - 0.035 . The wavelen4ths of intereHL with Ohw
indiceF of refraction and Rayleigh cross sections [computed frnm I'Pqs. (1) and (.))j
are listed in Table 1, and plotted in Figures I and 2.
Using the scattering cross sections, the linyleigh coefficients art obtained
with
4
1.00030 -- 1 -rTFFT-r1T
1.00029
3 1.00028-
1.0002 I I I 01
1010( WAVELENGTH (MICRONS)
Figure 1. Index of Refraction for 1013 mb and 150C (Table 1),IoTO RepreSent Attenuation Model Wavelengths
IOC0-26
10-27io2
10 30 1 1-2 1 1
WAVELENGTH (MICRONS)
rigu4re 2. Rayleigh Cross Section vs Wavelength (Table I),uouo Represent Attenuation Model Wavelengths
II
r •MX) r 00 N r(h) (10 cm/kr) (3)
where
Or = the Rayleigh attenuation coefficient (km"i)
Or 2 the Rayleigh scattering. cross section (cm2),
N r * the molecular number density (cm- 3)
The values of N (h) needed for Eq. (3) were obtained from the U.S. Standardr
Atmosphere and are listed in Table 2. This expression is used to compute an array
of Rayleigh attenuation coefficients as a function of altitude for each wavelength.
With the Rayleigh attenuation coefficients determined, the optical thicknessesfrom sea level to some altitude h are computed by
h
Tr(h,,) - )".r(hx)Ah , (4)
0
where5Tr* Rayleigh optical thickness (0 - h)
r mean of the Rayleigh attenuation coefficients (kmfor each altitude increment,
A h altitude increment chosen as one km for the.e calculations.
The Rayleigh optical thickness for altitude h to space is obtained by the rela-
tionship
r I (h X h r ,- 1r(hX) , ()
where
7(h) a Rayleigh optical thickness (h-)
r() = Rayleigh optical thickness (0- a* )'
r0km Abv80inStrlt(96cacltosbaeonN, adThe term rr(oo) was obtained by using Eq. (4) with the limits set between 0 and-80 kmn. Above 80 kmn, Stergis' (1966) calculations, based on N 2- 0 2 ,and 0 s
the principal atmospheric constituents, yield
. 0-6 , ), = 0. 4;f. pr(h,),) d 6. 7 •.X 107 X =0.61A
80 2.1X 10-7 X= 0 . 8M
These values approximate a constant 10" , that of the Hayleigh optical thickness
for unity air mass. For our purposes then the integral can be neglected because
the constant is small and applies to all wavelen-",q of interest.
Table 2. Model PnranspterR mR a Function of Altitudc
h (kim) Nr (cm" 3 ) D3 (cm/km)r 33
0 2.547 X 10 1 9 3.56 X 10-ý1 2.311 3.26 ,2 2.093 2.933 1.891 2.504 1.704 2.265 1.531 2.216 1.373 2.167 1.227 2.238 1.093 18 2.289 9.712 X to 2.81
10 8.598 3.5011 7.585 4.6012 6.486 6.2113 5.543 8.4514 4.738 9.5715 4.049 9.94 -216 3.461 1.03X 10 2
17 2.959 1.1118 2.529 1.2219 2.162 1.4220 1.849 1.6421 1.574 1.8422 1.341 1.97
2' 1.144 17 1.98,24 9. 760 X1t 1.9325 8.335 1.8026 7.123 1.6327 6.092 1.4128 5.214 1.2329 4.466 1.0730 3.828 9.03 X 10 3
31 3.283 7.9332 2.818 6.8233 2.406 5.8234 2.056 4.8535 1.760 4.3136 1.509 3.6137 1.296 3.0238 1.110, 16 2.5339 9.620x to 2.1740 8,308 1.86
41 7.187 1.5242 6.227 1.19 443 5.404 9.30 X 10 4
44 4.697 7.4445 4.088 5.7646 3.564 4.4647 3.112 3.5348 2.738 2.7949 2.418 2.2350 2.135 1.86
h- Altitude; Nr - Molecular number density;D 3 - Ozone equivalent thickness
1 73. ABSORPTION PARAMETERS FOR ATMOSPHERIC OZONE
This section is a summary of the material used in the 1964 Attenuation Model.
The parameter for determining 03 absorption as a function of altitude is the
atmospheric ozone absorption coefficient expressed by-
3(h,) ( , (6)
113 = atmospheric ozone absorption coefficient (km 1 ),
AV the pure ozone absorption coefficient (cmn ) after Vigroux,
D the ozone equivalent thickness (cmakm). .
Thus, the Vigroux coefficients (1953) listed in Table I in conjunction with the ozone
concentrations, Table 2 and Figure 3, permit the computation of an array of atmos-
pheric ozone absorption coefficients to 50 km for each of the desired wavelengths.
40
TOTAL OZONE&O.S5cm
F/
0 4 8 12 16 20 24
03 (cm/km x 10-3
Figure 3. Representative Atmospheric OzoneConcentration Profile (Table 2). Values for:0 to 30 kin, based on Handbook of Geophysiles
and Space Environment (1965)30 to 40 kmn, interpolated40 to 50 kin, based on London, Ooyama, and
Prabhakara (1962)
I
8
The ozone optical thickness from sea level to altitude h, 7 3 (h 0 ), and the
ozone optical thickness from some altitude h to space, r'3(h,7,), are included in
alie model tabulations. 4'I ne expressions for deriving these parameters have the
same form as Eqs. (4) and (5).
4. AEROSOL ATTENUATION
Of the various methods used to investigate aerosol attenuation, for the present
we will consider optical techniques only because they are suited to this type of study.itl In this country, Newkirk and Eddy (1964) used solar aureole photometry; Penndorf
(1954) analyzed solar radiation measurements from aircraft altitudes; Elterman's
results (1966a,b), with searchlight probing, comprise a substantial number of pro-
files acquired in New Mexico for altitudes to about 34 kmn. In Australia, Crosby
and Koerber (1962) used a balloon-borne integrating nephelometer. In the U. S. S. R.,
"Kondratiev, et al. (t967), conducted balloon solar transmission measurements;
Feoktistov (1965) analysed photographs of the earth's horizon from the spacecraft
Voschod; Rozenberg, et al. (1960) (1966):, acquired their results with searchlight
probing. 'rhe various pesults, as shbwn in Figure 4, were made comparable at.
;k - 0,. 55j& by using ,tKt empi.cal relationship that the aerosol attenuation codfft-
cient is inversely prlo ptrtidnal to wavelength. For reasons of clarity, a substantial
body of results W0 not included in Figurq 4,'as for example the twilight measure-
ments by Rosenberg (1965), Volz and Gocidy (1962), the searchlight measurements
by Spankuch (1967), analysis of twilight aýreole photographs from. the spacecraft
Vostok-6 by Driving (1966), the aircraft measurements of sky brightness by San-
domirski, Altovskaia and Trifonova (1964), and aircraft nephelometry by Waldram
(1945). Also, interesting results in the form of relative values have been obtained
with optical techniques: the twilight measurements byBigg (t 964), the laser beam
backscatter by Collis and Ligda (1966), by Clemeshaw, Kent, and Wright (0967),
and by Grams and Fiocco (1967)..
A consideration of all results shows, \as does Figure 4,. that the aerosol atten-
uation coefficient is a strongly fluctuating parameter and that average values based
on an adequate number of measurements are necessary in order to establish a repre-
sentative profile. The recent searchlight probing measurements (Elterman, 1966a
and 1966b) appear representative based on several considerations. First, each
profile was acquired by continuous measurement through both troposphere and
stratosphere and.with an altitude resolution approximating one km. In addition, a
total of 119 profiles comprising absolute -values of aerosol attenuation coefficients
were determined for various times throughout the year. This represents a sub-
stantially larger sample than previously published. Further, such a quantity of
,*1
9I10 7.-IIII
0
0
0 00++ AA
I&.O46+ A
* OoX++
o• • + ..-104 X4
U. x ,OA
A C"A++
Z X +++
W +0 40
L1J~~ ",,X44+ •
xx O
0 / 5 10 15 20 25 30 35
"• ALTITUDE (kin) O
Fire 4. Aerosol Attenuation Coefficients vs Altitude at 0. 55p.Co parison of results:x X X solar aureole, 2 balloon flights, Newkirk and Eddy (1964):
' solar radiation measured from aircraft, mean of 8 flights,Penndorf (I.954);
+ +++ + searchli ht probing, mean of 105 profiles, Elterman(1966a) and (1966b);
"me w ® balloon integrating nephelometer, mean of 14 flights, Crosby/,, and Koerber (1962);*,so e•a solar radiation measured from balloons, mean of 3 flights,/ .., Kondratiev et al. (1967);\spacecraft horizon photography, analysis of 4 frames,: Rozenberg (1966),
oeoktistov (l965);
/ o d,o searchlight probing, mean for 5 nights, lHozenberg (1966)
14.i ,
10
results readily permits statistical treatment. Finally, we note that the mean of the
119 profiles falls reasonably well within the values determined by other researchers,
a circumstance which tends to provide a meas.ure of comfort.
In considering the suitability of the 119 proofiles, ýextensive averaging is re-
quired and this tends to wash out features easily noted in the individual profile.We present, therefore, in Figure 5 a single profile, chosen because its properties
are readily evident and also because it is similar to the overall average. The fea-
tures can be made to emerge more prominently if the aerosol coefficients are used
to compute a turbidity profile, tp(h,1 I7N p (h, X )/Or(h, X) , where 0P and Pr are
the aerosol and Rayleigh coefficients respectively and X I 0. 55w (Figure 6).
Since volcanic dust in the atmosphere can have a residence time of several
years, the effects of the Mt. Agung eruption (March 1963) must be considered.
'The direct measurements of Junge, Chagnon, and Manson (1961), Friend (1965),
Mossop (1964), and Posen (1968), collectively considered, before and after this
event, show evidence of change in the stratospheric aerosol content. The observa-
tions of the twilight sky by Volz (1965) and Meinel and Meinel (1964) also show
augmentation of stratospheric particulates. Since the searchlight probing measure-ments yielded absolute values of aerosol attenuation coefficients, the most suitable
parameter to use for examining this feature quantitatively is tne stratospheric
aerosol optical thickness for the altitude region between the tropopause and 25 km.
The reason. for choosing the latter altitude limit will be discussed later, Accord-
ingly, all profiles were placed in time-sequential groups determined by the simi-
larity of the stratospheric-dust feature. Then the optical thickness was computed by
n 2
1F IN A p( h ,(7)
iml' hI
where n is the number of profiles in the group, h1 is the altitude of the tropopause,
h2 the 25 km altitude, 1' the mean aerosol attenuation coefficient (within each pro-
file) for the altitude interval, and Ah the altitude intervals used for computing
the profiles. The results of this computation are presented in Table 3. The tabu-
lation demonstrates a relatively high level of stratospheric dust for the December
1963 to March 1964 period. Beginning with April 1964, dust abatement and a gen-
erally stabilized level are in evidence. The mean optical thickness of Group (B+C+D)
is 26 percent less than that of Group A. Since Group A entails a period of abnorm-
ally high aerosol content, its profiles are not representative. These results are
in satisfactory agreement with the findings from the direct measurements of the
authors mentioned.
/
+ + +I+ +
i+
4'
20- +++
S1 ÷÷÷AEROSOL +++•:!.--. MOiECULAR :
30 -4.• ''•4N.
2 +
20
10-6 10-5 104 10-3AR O
ATTENUATION COEFFICIENT (krn"1
Figure 5. Single Profile]p,(h,? It) for I I April 1964 at 02:00 MST,Similar to Mean of 79 Profiles, XI w 0.,55,Surface to 5 kmn- convective region;5 to It.7 kmn- troposphere dust layer;
It. 7 to 23.,8 kmn- stratosphere dust layer,25.6 km - upper altitude maximum. . A E aerosol (measurements)
S molecular of pried)moeua computed)
i12
40 -
30 -4,
+
30- 4.
25- 4.44,
+
4..
taJ +
Is2_ 4-4
+ 4. 4 -.
++
10- +÷•, • • ÷ ,4.
4.4
S4 -.... 4 ,.4.
00*~ TURBIDITY p$
Figure 6. Single Turbidity Profile fi (h,;k )/0(h,),1
P' t
for It April at 0200 MST.+++4+ Measurements,(See caption pertaining to Figure 5)
oI.,
13
Table 3. Aerosol Optical Thickness as a Measure of Volcanic Dust, XI- 0. 5 5 jM
Period Number of Mean Optical ThicknessGroup (Inclusive) Profiles (approx. 12-25 kin)
A Dec 1963- Mae 1964 40 3. 1 X 10-2
B Apr 1964 50 2.2
C Oct 1964- Nov 1964 10 2.7
D Dec 1964-Apr 1965 19 2.4
B+C+D Apr 1964- Apr 1965 79 2.3
The considerations discussed above Justify the selection of the Group (B +1D)
profiles as a basis for developing representative aerosol attenuation pararnete'rs.
It will be convenient to designate the 7d profile average for X 1 0 O. 55 P as
p(h,l) (Figure 7). This profile can be extended to encompass a larger altitudep
range by using the scale height relationship,
p t3( 2 0% 1) ~~h2 ,x I exp - H2 h (8)p,.
Penndorf's study (1954) shows that for the lowest 5 km, the aerosol coefficients fall
off exponentially with a scale height 0.97 < I < 1.4 km. We resort to the use of
his mean value, Hp -1.2 km,' to extend the 9 (h1, X profile from 3.7 km to sea
level. This results in aerosol coefficients which are identical to those of the 1964
Attenuation Model for altitudes 0 to 3 km (Table 4.11).
Above the convective region, up to the tropopause the aerosol coefficients show
a moderate gradient which is in close agreement with Penndorf's analysis (1954) of
the vertical distribution of aerosols in the troposphere. Also, this section of the
profile is based on high signaJ to noise measurements and extensive averaging,
factors which contribute to its reliability. Additionally, this altitude region, being
above the convective layer, is cuiaracterized by aerosol conditions which tend to be
independent of surface terrain. These considerations suggest that the shape and
values of the p(h, XI) profile for this altitude region are realistic.
Above the tropopause, up to 25 kin, the coefficients are larger than those de-
rived for the 1964 Attenuation Model by a factor of about 20 (at 20 km for Xl 0. 5 5P ).
This difference may be attributed in part to the intrinsic difficulties of converting a
size distribution to an optical parameter, that is, establis hing the radii limits,
particle shape, chemistry, and index of refraction. H,' itiv, to profile shape, a
turbidity maximum dominates at about 1.) km ( I'igure 8). '[lie measurenients of
Rosen (1968) and those of Volz (19611) for 1.964 to 19611 are, in smtisfactory agrecr1.ent
I
4'm
14
lot
T 4,
4. ,.4 ÷i
eillCQ"II
. M.4
35, ,
II4.
4,
30- 4
44
Ol 20O
25 +
+
4o
15 -
S4.
20
Fiur 0. MenTridt rf
* 1 ( )4)
( t F
4,.
10 44.4.
4.4.
o - , 4. 4. . .
0 I.0 2.0 3.0TURBIDITY ,Gp/•Gr •
Figure 8, Mean Turbidity Profile, •p(h, X)/1 3(h,•l(See caption for Figure 7) Par
16
with the mean optical thickness and shape of the Group (B ýC+D) profiles. Table 3.
Afin their resultR ghow that the stratospheric dust level has remained approximate-
ly constant from 1964 to the time of this writing. The ý p(h,AI) curve (Figure 7)
shows this dust feature as the knee of the profile rather than a massive layer fea-
ture indicated by the turbidity profile. This conceptual relationship suggests thatover-emphasis is possible when dealing only with turbidity profiles.
The turbidity profile shows an upper stratospheric maximum with its lower
terminus at 25 km. This altitude then, was the basis for choosing the upper strato-
spheric dust limit in Eq. (7). The maximum at 26 km occurs with sufficient fre-
quency to be easily identified in the turbidity profile. The existence of such all
aerosol concentration above 20 km is supported by the analysis of satellite photog-
raphy reported by-Mateer, Dave, Dunkelman, and Evans (1967).
To establish upper altitude aerosol coefficients, a least square fit was com-
puted for ý (h,X 1 ) from 26 to 32 km (Figure 9). The result, Hp = 3.75 km (in
effect derived from 790 measurement points), was used in Eq. (8) to extend the
values to 50 krm. Miller (1967) obtained H. = 3.25 km from a thorough analysis
of rocket measurements acquired in 1964 for this altitude region. The overall
profile from sea level to 50 km is presented in Figure 10 (Table 4. 1 t). Since the
lo*'S , I I i I I '
"I10,,
S,-
4n02 26 28 '30 32ALTiTUCE (kin)
F'igure 9, E;.xpanded Sc~ale for 26 to 32 km Altitude RegionShowing lip = 3•75 km for 79 Profile Mean; AerosolAttenuation Coefficients, I3D(h.X 1 ) va Altitude; LeastSquare Vit Used to Extrarolate to 50 kin; X'7 --9.5
I' S 17
50 .
MOLECULAR
40
530
AEROSOL AEROSOL20 1964 ~19683
10-
ATTENUATION COEFFICIENT (ký'
liigure 10. Comparison of Profiles. Aerosol attenuation coefficientsPp(h, Xj) , with molecular gr(h. Xi). The 1964 profile shows interpola-tion between 5 to 10 kin; X10 55
18
turbidity is proportional to the mixing ratio, the diminishing values for the extrapo-
origin, the mixing ratio would tend to be constant or increase for altitudes 30 to 50
km.
Thus far we have selected a set of measurements for X, - 0.55p and provided
reasons for 'ts use. It would be in order now to examine some expressions leading
to corresponding aerosol profiles for other wavelengths. If we consider a real
atmosphere, the aerosol sizes within unit volume can be described by a size dis-
tribution function, * (r) . Various size distribution functions are in use: the Junge
type power law (1963) with a choice of exponents discussed in detail by Bullrich
(1964), a similar distribution modified by gaps observed by Fenn (1964), a log-
Gaussian distribition used by Foitzik (1965), a composite distribution with com-
ponents from several types. The optical-particle size relationship utilizes O(r)
such that
N
p(mr,,) -f Ia(m,r,X) dN(r) (9)p p p
N
dNp -N 0 O(r) dr (10)
No(h) C Np(h) . (11)p
1P is the aerosol attenuation coefficient, m is the index of refraction, Nrl and
Nr 2 are the aerosol number density limits established by the radii limits r 1 and
r2 , ap is the aerosol cross section for each particle, Np is the total number of
particles between r 1 and r 2 - For a given altitude, N actually is proportional
to the particle number density-between r 1 and r 2 . Since the same size distribu-
tion function applies to all altitudes (an assumption), Eqs. (9), (10), and (11) are
combinedr 2
p(hA) = CN (h) f op(rX) d(r) dr . (12)r1
Here, C N p(h) is placed outside the integral which now contains only factors that
are independent of altitude; also, m is removed because subsequent considera-
tions will pertain to particles without any distinction in refractive index. If
Eq. (12) is normalized to sea level conditions, the integral cancels out. Then
generally for the various wavelengths X, and specifically for 1= 0. 55p we have
II
N!j3.._(h,)X) &_(h. X,) N (h) (3
or
Pp(hX) p (0, . p(h,A1) (14)
Equation (13) has been derived in this manner to demonstrate its compatibility with
particle size considerations. Sea level conditions have been researched extensively
by Curcio and Durbin (1959), Curcio, Knestrick, and Cosden (1961). Knectrick,
Coaden, and Curcio (1961), Dunkelman (1952), Baum and Dunkelman (1955). The
P,0(0,X•) values for a 25 km M.R., based on the results of these authorsare shown
in Figure 11 (see also Elterman, 1964). Utilizing these results, in conjunction
with the Ip (h, k1) profile (Table 4. 11), all requirements for the right-hand side
of Eq. (14) are satisfied and an array of aerosol attenuation coefficients can be
computed for all altitudes and wavelengths of interest.
The aerosol optical thickness from sea level to altitude h, r (h, X) , and the
aerosol optical thickness from some altitude h to space, .'(h, X, are included inp
the model tabulations. The expressions for deriving these parameters have the
same form as Eqs. (4) and (5).
i~~~~~ Sxl' .... - ,I
r If ! "
5 X 10"
16.1
2K1020.1 0.2 Q.3 0.5 1.0 2.0 4.0
WAVELENGTH (microns)
Figure 11. Aerosol Attenuation Coefficients •u(O, ) vsWavelength at Sea Level for a Meteorological RangeApproximating 25 km.A - derived from Baum and Dunkelman (1955)B - contained in Curcio, Knestrick, and Cosden (1961)
20I
. .V%0SIOPIIERIC EXTINICTION
In this section, three sets of extinction parameters are considered: extinction
coefficient, extinction optical thickness from sea level to a desired altitude, and
extinction optical thickness from a desired altitude to space.
The atmospheric extinction coefficient ext is the sum of all the attenuating
components:
•ext(h,?,) Pr(hX) + 003(h,A) + Ph,•) .(15)
The extinction optical thickness from sea level to altitude h , Next(hX) , and
the extinction. optical thickness from some altitude h to space, rTxt(h,X ) , are in-
cluded in the tabulations of the attenuation model, The expression for deriving
these parameters has the same form as Eqs. (4) and (5).
6. EXPLORATORY TRANSMISSION CALC•IATIONS
Using the derived tabulations that follow, some explopatbry calculations withextinction parameters (for any of the wavelengths) are,/demonstrated. Rayleigh,
aerosol, and ozone parameters can be used similarly.
For horizontal transmission (Th) over a path (d) at any altitude (h) , the ex-
tInction coefficient
STh exp [ -Pext f(h,X ),d d (16)
For -vertical and slant-path transmission from sea level to a given altitude,' at
zenith angle a for all wavelengths of interest
To- = exp [- Tet (h) -seae] (17)
For vertical and slant-path transmission between two altitudes above sea level
T Ah ' exp - [ext(h2) - 7'ext(hl). sec 0 (18)
For vertical and slant-path transmission from a given altitude out into space
T =x e'xt(h) sec 0 (19)
/
I
21I ~~7. C:ONC:LUDlING REMARKS•
The procedure for developing the aerosol attenuation profile is summarized as
follows :
(1) Various studies were compared and of these a set of measurementsselected.
(2) The choice of measurements (comprising 119 profiles from 2.76 to 34.4 kin)
was examined statistically. This resulted in the elimination of 40 profiles
(December 1963 to March 1964 inclusive) characterized by a high volcanic
dust component.
(3) The mean of the 79 remaining profiles was extended to sea level and to
50 km respectively by reasonably supported extrapolations.
(4) The overall profile then was developed laterally to obtain 21 additional
profiles for the wavelengths of interest.A significant aspect of the procedure is that the wavelength--height array of param-
* eters was derived independently of the assumptions associated with conversion of
a size distribution to an optical parameter.
For most purposes, calculations using the new parameters will be affected
only moderately. For example at X 0,, 55BA , the 1964 Attenuation Model providesan extinction optical thickness, text 0. 331, for a vertical air mass. The new
parameters yield Text = 0.379, resulting in a transmission change of about 3-1/2percent. However, for long path horizontal transmission calculations above 5 km
and for long slant-path calculations entailing large zenith angles, the new aerosol
parameters can function more significantly.
As mentioned previously, the Hayleigh and ozone parameters are unchanged.
8. TABULATION O' PARAMETERS
Tables 4r1 to 4.22, which follow, comprise the atmosph.eri- attenuation model.
Exponents are in computer notatlona for example, read 2,86-3 = 2.8 8 X 10 and2.86 3 as2.86 X 103
.I
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45
Acknowledgments
The author would like to acknowledga th helpful review provided by R.W. Penn,
1R. Penndorf, and F. Volz. Appreciation is xteided also to H. Wexler and
D. Chang for their discussions pertaining to meteorological aspects and to
R. Hoffman and J. LPuseo for their particip tion with computer programming.
I.Ii.
I
47
References
,Baum, W.A. and Dunkelman, L. (1955) Horizontal attenuation of ultraviolet lightby the lower atmosphere, J, Opt. Soo, Am. 456 188.
Bigg, E.K. (1964) Atmospheric stratification revealed by twilight sca.ttering,Tellus. 1677-83.
Bullrich, K. (1964) Scattered radiation in the atmosphere and the natural aerosol,from Adv. in Geooh sics. 10: 101-257, H.E. Landsberg and J.E. Mieghem,Editors, Academic Press,"FY.
Clemesha, B.R., Kent, 0.S., and Wright, R.W. '(1967) A laser radar for atmos-pheric studies, J, Appl. Meteorol, 6.386-395.
Collie, R.T.H. and Ligda, M.G.H. (1066) Note on Lidar observations of particu-late matter in the stratosphere, J. Atmos. Sci. 2 3:255-257.
Crosby, P. and Koerber, 13.W. (1962) Scattering of light in the lower atmosphere,J. Opt. Soo. Am. 53:358-361.
Curoio, J.A. and Durbin, K.A. (1959) Atmoseheric Transmission in the Visible'Region NRL Rpt 5368, U.S. Naval liesearoh Laboratory, Washington, D.C.
Curclo, J.S., Kneetriok, G.L., and Coaden, T.!1. (1961) Atmospheric ScatteringIn the Visible and Infrared. NHL Rpt 5567, U.S. Naval Research Laboratory,Washington, D.C.
Driving, A.Y. (1966) IZV. Atmospheric and oceanic physics, Vol. 2, No. 10,pp. 1046-1054 (U.D.C. 551.593.5:629.195).
Dunkelman, L. (1,952) lIorizontal Attenuation of Ultraviolet and Visible Light b.,the ower Atmosphere, NRL lipt No. 4031, U.S. Naval Research Iaboratory,Wash~ington, D.C.
Edldn, B. (1953) The dispersion of standard air, .,J. Opt. Soc, A\m. 43.330.Elterman, L. (1964) Atmospheric Attenuation Model, 1964, in the Ultraviolet,
Visible, and Infrared Regions for Altitudes to 50 km, Report Ai'C•L-64-.740,AFCRL, Bedford, Mass.
48
Refegrences
Elterman, L. (1966a) Aerosol measurements in the troposphere and stratosphere,Appi. Opt. 5, 1769'.
Elterman, L. (1966b) An Atlas of Aerosol Attenuation and Extinction Profiles forthe Tro osphere aind Stratosphere Report AFCRtL-66-828, AFCRL, Bedford,Mass.
Fenn, R. W. (1964) Aerosol-Verteilungen und atmospharisc hes Streulicht, Bje.flagezur Physik der Atmosphare, 34(No. 2): 69.
Fenktistcv, K. P. (1965) Some results of optical observations from a Voskhodspacecraft, in-, G. A. Skuridin, et al., eds. Issledovanila komicheakogoprostranstva (Investigations of Cosmic Space). Moscow , Izd-vo "Nauka"',
Foitzik, L. ( 1965) The spectral extinction of the atmospheric aerosol by Mieparticles with different Gaussian distributions, Gerlands Beitrage zur Geophysik
73feft 3, 199,Friend, J. .. (1985) Propertiea of thre S71trao.heri AerosoL Isotopes, Inc.,
Report for contract D~A-49-i 6-Z0 ne Aomic Support Agency (U)2 N ov.
Grams, G. and Fiocco, 0. (1987) StratogpIheri'ý aerosol layer during 1964 find t965,J6. Geophys. Res... 72 13523-3542.
Gucker, F. T6 an asu, S. (19B3) Ri hfttangle Molecular Light Scattering fromGms iRtN.1Cotat 172-2).'.4-00, U._of Indiana.
June.,C~E. CagnnC.W., and Manson', J.E. (1061) Stratospheric aerosols,
Jung, C'E.(193) Ar CemitryandRadioactivity, Aaei rsNYKneoric, G L. Coden T.HiandCurcio, J, A. (19601) Atmoin heric Attenua-
tion Cefficients!.An the Visble and Infrared, N'RL Rpt 5648, U.S. Naval ResearchCET-o-&Fry, Wastington, D.Q,
Kondratiev, K. Ya. , Nicolsky, G.A. , Bsdinov, I. Ya.,- and Andree-v, S.D. (1067)Direct solar radiation uip to 30 kmn and stratificat ion of attenuation component.in the stratosphere, Appl. Opt.6 81197.
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References
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' ' !
S-
UnclassifiedSecurity Classification
DOCUMENT CONTROL DATA - I&D(Se.uril cl dasslflcation of tille, body of abstruo and indeamne annoijoin must be enteed whom sAh .n'vmll !eport is classifled)
I. ORIGINATING ACTIVITY (Cofatho t ml~o) - |0. L REPORT SECURITy CLASSIFICATION
Air Force Cambridge Research Laboratories (CRO) UnclassifiedL. G. Hanscom Field 2 GROUPBedford, Massachusetts 01730
3. REPORT TITLE
UV, VISIBLE, AND IR ATTENUATION FOR ALTITUDES TO 50 KM, 1968
4, O"ScmipTivi NOTES (Type ofeporn and inclus.i da•tsezScientific. Interim.
S. AUTI4ORWS (First snme, W m iddleiIal. last now,)
Louis Elterman
S, REPORT OATE 79h TOTAL NO. OF PACKS 0 NcoPrEApril 1968 56 45go. CONTRACT OR GRANT NO. ,, . ORIGINATOR'1 REPORT NUNSEWIi )
4 J6 EROJACS, TASK. WORK UNIT NO$, 7670-04-01 M. ' AFCFtL-68-0153
a. 000 ELEMENT 6240539F! oh ob•. 0T JPoIRT js),(Ary oA.,,mube, Mts nuy b
A POD. sUILEMEMT 681000 ERP No. 285
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1 - Distribution of this document Is unlimited. It, may be released to theClearinghouse, Department of Commerce, for sale to the general public.
III 1UPPLEMENTARY NOTES IS SPONSORING MILITARY AVTVITY
T H TEi Air Force Cambridge ResearchLaboratories (CRO)
L. G. Hansoom FieldBedford, Massachusetts 01730
t iII, AEIITRACI
\An atmospheric attenuation morel for the ultraviolet, visible, and infrared wasdeveloped in 1964, based on scattering (molecules and aerosols) and ozone absorp-tion. Since then more'measurements have been made and our knowledge of aerosol"attenuation has widened. These circumstances result in attenuation model changeswhich are relatively unimportant for most exploratory calculations. They can be sig-nifioant, however, for long slant-path high-altitude applications entailing large zenithangles, factors which characterize, for eyample, the measurement geometries ofrockets and satellites. Anoordingly, a revision of the 1004 Attenuation Model iswarranted.
In this paper the optical parameters are computed spectrally and with altitude asfollows: (1) pure air attenuation parameters are determined by utilizing Rayleighscattering cross sections with molecular number densities from the standard atmos-phere; (2) ozone absorption parameters are derived based on VigrouxIs coefficientsapplied to a representative atmospheric ozone distribution; (3) seven sets of aerosolmeasurements are compared and a profile of aerosol attenuation coefficients vsaltitude is developed. Attenuation coefficients and optical thickness due to molecular,aerosol, and ozone attenuation are computed and tabulated individually so that theinfluence of each can be compared. The newly derived tabulations permit variousexploratory calculations, including horizontal, vertical, and slant-path transmissionat kilometer intervals to an altitude of 50 kin, individually for each attenuating com-ponent or for overall atmospheric extinction (molecular + ozone - aerosol),
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I
UnclassifiedSecurity Classific•tion
, K RLINK A LINK a IINK CKEY WOROS ___
ROLE WYr ROL WY ROLE W?
UV atmospheric transmissionVisible atmospheric transmissionIR atmospheric transmissionAerosol atmospheric attenuationTransmission in troposphere and stratosphereAerosol attenuation in troposphere
and stratosphereModel atmosphereLight scattering
T 1nelassifik-td
Sr - Q i
I t1 aH' l