Open Journal of Applied Sciences, 2013, 3, 490-513
Published Online December 2013 (http://www.scirp.org/journal/ojapps)
http://dx.doi.org/10.4236/ojapps.2013.38059
Open Access OJAppS
Numerical Analysis of the Analytical Relationships between
Angstrom Coefficients of Aerosols and Their Optical
Properties for Four Types of Aerosols
Bello Idrith Tijjani1, Sha’aibu Uba2, Fatima Salman Koki1
1Department of Physics, Bayero University, Kano, Nigeria
2Department of Physics, Ahmadu Bello University, Zaria, Nigeria
Email: idrith@yahoo.com, idrithtijjani@gmail.com, shuba356@yahoo.com,
shuba356@yahoo.com, FatimaSK2775@gmail.com
Received September 30, 2013; revised November 2, 2013; accepted November 10, 2013
Copyright © 2013 Bello Idrith Tijjani et al. This is an open access article distributed under the Creative Commons Attribution Li-
cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In
accordance of the Creative Commons Attribution License all Copyrights © 2013 are reserved for SCIRP and the owner of the intel-
lectual property Bello Idrith Tijjani et al. All Copyright © 2013 are guarded by law and by SCIRP as a guardian.
ABSTRACT
In this paper, the authors numerically analyzed the analytical relationships between angstrom coefficients and optical
properties of aerosols to the existing data extracted from OPAC at the spectral length of 0.25 μm to 2.5 μm at eight rela-
tive humidity for desert, urban, marine clean and continental clean aerosols. That is apart from their relationships with
the wavelength that was determined, in this paper their relation with respect to aerosols’ type and RHs are determined.
The properties extracted are scattering, absorption, and extinction coefficients and single scattering albedo. The results
showed that the extinction and single scattering albedo are correct for all the aerosols but single scattering co-albedo is
satisfied for only sahara and continental clean.
Keywords: Angstrom Coefficients; Analytical Relationships; Parameterize; Wavelength Dependence; Optical
Properties
1. Introduction
The Angstrom exponent (AC) is a parameter that is being
widely used in atmospheric sciences to analyze the opti-
cal properties of aerosol particles. Since the early publi-
cations of Angstrom [1,2] and his later publications [3,4],
where this parameter was mainly applied to the descrip-
tion of the spectral behavior of the atmospheric extinc-
tion and transmission, respectively, it is now being ap-
plied to a variety of similar but slightly different optical
properties, for instance to the atmospheric, optical depth,
extinction coefficient, scattering or backscattering coef-
ficients etc. It is very popular not only because of the
simplicity of the equation, but because it enables ex-
trapolation or interpolation of aerosols’ optical properties,
because it is connected to particle microphysics (related
with the mean size of aerosols) as it describes, approxi-
mately for a certain radius range, and a spectral range, a
power law (Junge) aerosol size distribution [5-8]. It was
refined by O’Neill and Royer [9] who derived bimodal
size distribution radii using these parameters.
The Angstrom exponent being an indicator of the aero-
sol spectral behaviour of aerosols [10], has been adopted
by a number of authors in the literature to characterize
biomass burning aerosols [11,12], urban and desert dust
aerosol [13] and maritime aerosols [14]. In general, the
aerosol optical depth (AOD) and AC parameters can be
used to differentiate between coarse and fine particles
[15].
Simple analytical relationships between extinction, scat-
tering, and absorption coefficients and single scattering
albedo (SSA) [16], and the corresponding relationships
for ACs [17] exist. Such relationships are useful to com-
pare ACs obtained from extinction, scattering, and ab-
sorption, including the ground truthing of remote sensing
and satellite measurements. For example, aerosol extinc-
tion can be obtained from ground-based and satellite re-
mote sensing at multiple wavelengths yielding extinction
Angstrom coefficients (EACs). Simple analytical rela-
tionships between EACs, scattering Angstrom coefficients
(SACs), and absorption Angstrom coefficients (AACs)
B. I. TIJJANI ET AL.
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491
will help attribute the EACs to the underlying physical
phenomena, namely scattering and absorption, and ana-
lyzing closure between the different Angstrom coeffi-
cients. In addition, SSA is the key parameter that nor-
mally determines the sign and magnitude of aerosol ra-
diativeforcing. SSA can be obtained at multiple wave-
lengths from in-situ measurements [7,8,18], ground-based
remote sensing measurements [19,20], and potentially
from satellite measurements [21,22]. Relating the SSA
Angstrom coefficient (SSAAC) to the underlying SAC,
AAC, and EAC will help with data interpretation and
closure and physical understanding. The SSAs are some of
the most dominant input factors that determine the aero-
sols type in radiative transfer models [23-26] and depend
on the microphysical properties of the aerosols and there-
fore their value can be used for the characterization of
the aerosol type. SSA can be interpreted as the probability
that light will be scattered, giving an extinction event or
the ratio between the scattering coefficient and the ex-
tinction coefficient while the Single scattering co-albedo
(SSCA) can be considered as the probability of absorp-
tion per extinction event or ratio between the absorption
coefficient and the extinction coefficient. Therefore if
SSAAC is less than 0 it indicates that SSA increases with
wavelength, while if SSAAC is larger than 0, SSA de-
creases with wavelength. This shows that SSAAC can be
used to determine the increase or decrease in the radia-
tive forcing and while for single scattering co-albedo
Angstrom coefficient (SSCAAC) is the reverse. From the
various plots we observed some spectral intervals where
SSA decreases with the wavelength as well as some spec-
tral intervals where SSA increases with the wavelength.
In addition, ACs can be obtained from simple linear or
nonlinear regression of data plotted on a log-log scale or
more complicated non-linear fits of data that may also
yield higher order terms which give additional informa-
tion about the type of aerosols using the curvature [27].
Relationships between different ACs that include the SSA
(ω) have only been derived by Moosmuller and Chakra-
barty, [17]as for single- and two-wavelength ACs, while
for ACs obtained from linear or non-linear fits the mathe-
matics gets much more complicated due to the difficulty
of appropriately attributing the influence of the SSA at
different wavelengths. However, in most cases, the sin-
gle-wavelength equations still give a good approximation
depending on the type of aerosols and relative humidity.
In aerosol optics, the ACs that are of most interest are
scattering, absorption, and extinction coefficients and for
the SSA (ω) and single scattering co-albedo (SSCA). The
relationships between these ACs are analytically deter-
mined by Moosmuller and Chakrabarty, [17] as:
Extinction Angstrom coefficient EAC
 
EACAACSAC AAC
 
 
(1)
Single Scattering Albedo (SSA) Angstrom coefficient
(SSAAC)

SSAACSAC EAC

 (2)
Single Scattering Co-Albedo (SSCA) Angstrom coeffi-
cient (SSCAAC)

SSCAACAAC EAC

 (3)
As suggested by Moosmuller and Chakrabarty [17], in
this paper we are going to apply these relationships to the
existing data extracted from OPAC at the spectral length
of 0.25 μm to 2.5 μm and eight RHs (0%, 50%, 70%,
80%, 90%, 95%, 98%, and 99%) for desert, urban, ma-
rine clean and continental clean to determine its accuracy
and its dependence on the types of aerosols, the power of
the polynomials and RHs (that is hygroscopic growth as
a result of the change in RHs).
2. Methodology
The models extracted from OPAC are given in Table 1.
The spectral behavior of the aerosol’s optical parame-
ter (X, say), with the wavelength of light (λ) is expressed
as inverse power law [3]:
Table 1. Compositions of aerosol types [28].
Aerosol model types Components Concentration Ni (cm3)
Urban
WASO
INSO
SOOT
Total
28000.0
1.5
130000.0
158001.5
Continental clean
WASO
INSO
Total
2600.0
0.15
26000.15
Desert
WASO
MINM
MIAM
MICM
Total
2000.0
269.5
30.5
0.142
2300.142
Maritime clean
WASO
SSAM
SSCM
Total
1500.0
20.0
0.0032
1520.0032
where: Ni is the mass concentration of the component, water soluble com-
ponents (WASO, consists of scattering aerosols, that are hygroscopic in
nature, such as sulfates and nitrates present in anthropogenic pollution),
water insoluble (INSO), soot (SOOT, not soluble in water and therefore the
particles are assumed not to grow with increasing relative humidity), min-
eral nucleation mode (MINM), mineral accumulation mode(MIAM) , min-
eral coarse mode (MICM), Sea salt accumulation mode (SSAM) and Sea
salt coarse mode (SSCM). Urban aerosol represents strong pollution in
urban areas. Continental clean aerosol represents remote continental areas
without or with very low anthropogenic influences. Desert aerosol is used to
describe aerosol over all deserts of the world, and no distinction with respect
to the local properties is made. It consists of the mineral aerosol components
in a combination that is representative for average turbidity, together with a
certain part of the water-soluble component. Maritime aerosol types contain
sea salt particles and Maritime clean is given to represent undisturbed re-
mote maritime conditions with no soot, but with a certain amount of wa-
ter-soluble aero-sol, which is used to represent the non-sea salt sulfate.
B. I. TIJJANI ET AL.
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492

X

(4)
where X(λ) can represent extinction, scattering, and ab-
sorption coefficients, single scattering albedo and single
scattering co-albedo while β is the turbidity and α is the
Angstrom exponent (AC) [9,29]. The wavelength depend-
ence of X(λ) can be characterized by the AC, which is a
coefficient of the following regression:

lnXln ln
 
 (5)
However the Angstrom exponent itself varies with
wavelength, and a more precise empirical relationship
between aerosol extinction and wavelength is obtained
with a 2nd-order polynomial [13,30-38] as:
 
2
21
lnXlnln ln

 (6)
Here, the coefficient α2 accounts for a “curvature” of-
ten observed in sunphotometry measurements. Eck et al.
[12,13], Schuster et al., [27], O’ Neill et al., [34] and
Kaskaoutis et al., [39,40] reported the existence of nega-
tive curvatures for fine-mode aerosols and near zero or
positive curvatures are characteristic of size distributions
with a dominant coarse-mode or bimodal distributions
with coarse-mode aerosols having a significant relative
magnitude.
Now differentiating Equation (5) with respect to lnλ
we obtained




dlnX
dln
 (7)
Also differentiating Equation (6) with respect to lnλ
we obtained





12
dlnX 2ln
dln

 (8)
Assuming that Equations (7) and (8) are evaluated at a
wavelength, this implies we can substitute Equation (7)
into (8) to obtain
 
12
12ln

  (9)
Equation (9) now shows the relationship between α
and wavelength.
We now also proposed a cubic relation of the form
 
23
12 3
lnXln lnlnln

   
  (10)
to determine whether cubic relation can improve the ac-
curacy of Equations (1)-(3).
Also differentiating Equation (10) with respect to lnλ
we obtained




 

2
12 3
dlnX 2ln3 ln
dln
 
  (11)
Assuming that Equations (7) and (11) are evaluated at
a wavelength, this implies we can substitute Equation (7)
into (11) to obtain
 

2
123
22ln3ln
 
  (12)
In this paper we are going to determine the correlation
of Equations (1)-(3) with Equations (7), (9) and (12) for
all the four types of the aerosols with respect to wave-
lengths and RHs. In Equation (1) since it involves prod-
ucts, we determined the average, but in Equations (2) and
(3), since they have linear relations, we compared the
coefficients.
3. Results and Observations
Figure 1(a) shows that power law is satisfied at 90%,
95%, 98% and 99% RH, but not satisfied at 0%, 50%,
70%, and 80%.
Table 2(a) shows good correlations at 90%, 95%, 98%
and 99% RH, but bad correlations 0%, 50%, 70%, and
80% RH for linear. The increase in the power of the
polynomials and RHs caused increase in the correlations.
Figure 1(b) shows that the plots can be approximated
by the power law.
Table 2(b) shows very good correlations, and the cor-
relations increase with the increase in the power of the
polynomials and RHs.
Figure 1(c), spectral extinction coefficients decrease
with wavelength and can be approximated with a power-
law wavelength dependence and also a bi-modal type of
particle size distributions [13]. The increase of the coef-
ficients with RH has occurred because of the increase in
mode size as a result of the increase in RHs. The increase
of the extinction with RH at the deliquescence point (90
to 99) is that the growth increase substantially, making
the process strongly nonlinear with RH [41,42].
Table 2(c) shows good correlations between extinc-
tion and
using Equations (5), (6) and (10). The correla-
tions increase with the increase in the power of the poly-
nomials and RHs.
Observing Figures 1(a) and Table 2(a), it can be seen
that at RHs 0% to 90% the scattering coefficients have
not satisfied the power law, and within this range it can
be observed that in Table 2(d), Equation (1) underesti-
mated Equation (7) on the linear part but overestimated
Equations (9) and (12) on the quadratic and cubic part
respectively at all the RHs. The gaps decrease with the
increase in RHs.
Figure 1(d) shows that the plots can be barely ap-
proximated by the power law.
Table 2(e) shows that the correlations decrease with
the increase in RH, but increase with the increase in the
power of the polynomials.
Comparing the coefficients at Tables 2(e) and (f) it
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0.5 1.0 1.5 2.0 2.5
0.1
0.2
Scattering Coefficients(km
-1
)
Wavelengths(
m)
SCATCO00
SCATCO50
SCATCO70
SCATCO80
SCATCO90
SCATCO95
SCATCO98
SCATCO99
Figure 1(a). A graph of scattering coefficients against wavelength for sahara at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
Table 2(a). The results of the Angstrom coefficients of scattering coefficients using Equations (5), (6) and (10) for sahara
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.0053 0.0101 0.9653 0.0819 0.2002 0.9829 0.0515 0.2349 0.0455
50 0.0800 0.0355 0.9537 0.1153 0.1738 0.9805 0.0812 0.2127 0.0510
70 0.2250 0.0606 0.9551 0.1349 0.1617 0.9817 0.1002 0.2012 0.0518
80 0.3960 0.0853 0.9606 0.1547 0.1511 0.9839 0.1203 0.1903 0.0515
90 0.6899 0.1389 0.9754 0.1997 0.1324 0.9890 0.1673 0.1694 0.0485
95 0.8629 0.2082 0.9887 0.2624 0.1179 0.9937 0.2362 0.1478 0.0392
98 0.9377 0.3124 0.9961 0.3655 0.1156 0.9967 0.3522 0.1307 0.0198
99 0.9488 0.3841 0.9978 0.4435 0.1293 0.9978 0.4399 0.1335 0.0055
0.5 1.0 1.52.0 2.
5
0.00
0.01
0.02
0.03
0.04
0.05
Absorption Coefficients(km
-
1
)
Wavelengths(
m)
ABSCO00 ABSCO50
ABSCO70 ABSCO80
ABSCO90 ABSCO95
ABSCO98 ABSCO99
Figure 1(b). A graph of absorption coefficients against wavelength for sahara at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
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Table 2(b). The results of the Angstrom coefficients of absorption coefficients using Equations (5), (6) and (10) for sahara
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.7568 0.8058 0.9684 0.5157 0.6315 0.9821 0.6961 0.8374 0.2698
50 0.7562 0.8050 0.9686 0.5144 0.6325 0.9821 0.6932 0.8365 0.2673
70 0.7559 0.8047 0.9687 0.5139 0.6329 0.9821 0.6921 0.8362 0.2665
80 0.7557 0.8043 0.9688 0.5134 0.6332 0.9822 0.6912 0.8360 0.2659
90 0.7551 0.8036 0.9689 0.5124 0.6340 0.9822 0.6896 0.8361 0.2650
95 0.7541 0.8025 0.9690 0.5108 0.6350 0.9822 0.6875 0.8366 0.2643
98 0.7519 0.8003 0.9690 0.5074 0.6375 0.9823 0.6843 0.8392 0.2645
99 0.7497 0.7979 0.9689 0.5040 0.6397 0.9824 0.6816 0.8422 0.2655
0.5 1.0 1.5 2.0 2.5
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Extinction Coefficients(km
-1
)
Wavelengths(
m)
EXTCO00
EXTCO50
EXTCO70
EXTCO80
EXTCO90
EXTCO95
EXTCO98
EXTCO99
Figure 1(c). A graph of extinction coefficients against wavelength for sahara at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
Table 2(c). The results of the Angstrom coefficients of extinction coefficients using Equations (5), (6) and (10) for sahara
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.8824 0.1225 0.9422 0.1442 0.0473 0.9880 0.0979 0.1001 0.0693
50 0.9411 0.1552 0.9624 0.1711 0.0346 0.9911 0.1261 0.0859 0.0673
70 0.9583 0.1733 0.9706 0.1867 0.0291 0.9922 0.1435 0.0784 0.0646
80 0.9697 0.1918 0.9770 0.2031 0.0247 0.9932 0.1620 0.0716 0.0615
90 0.9836 0.2320 0.9864 0.2404 0.0182 0.9948 0.2047 0.0588 0.0533
95 0.9916 0.2855 0.9932 0.2933 0.0169 0.9963 0.2670 0.0469 0.0393
98 0.9942 0.3684 0.9974 0.3827 0.0310 0.9977 0.3722 0.0430 0.0156
99 0.9914 0.4272 0.9985 0.4517 0.0535 0.9985 0.4520 0.0532 0.0004
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Table 2(d). The results of the Angstrom coefficients of extinction coefficients using Equations (1), (7), (9) and (12) for sahara
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) Equation (7) Equation (1) Equation (9) Equation (1) Equation (12) Equation (1)
Α Α α1 (λ) α1 (λ) α2 (λ) α2 (λ)
0 0.122451 0.101199 0.115492 0.159794 0.139420 0.141914
50 0.155226 0.136194 0.150135 0.189424 0.173392 0.175070
70 0.173292 0.155676 0.169010 0.206057 0.191334 0.192991
80 0.191773 0.175054 0.188141 0.222690 0.209395 0.210576
90 0.231990 0.217366 0.229310 0.259265 0.247712 0.248438
95 0.285518 0.273175 0.283026 0.307763 0.296618 0.296840
98 0.368436 0.359011 0.363871 0.382144 0.369275 0.368879
99 0.427181 0.419607 0.419313 0.433753 0.419175 0.418214
0.5 1.0 1.5 2.0 2.5
0.65
0.70
0.75
0.80
0.85
0.90
0.95
Single Scattering Albedo
Wavelengths(
m)
SSA00
SSA50
SSA70
SSA80
SSA90
SSA95
SSA98
SSA99
Figure 1(d). A graph of single scattering albedo against wavelength for sahara at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
Table 2(e). The results of the Angstrom coefficients of single scattering albedo using Equations (5), (6) and (10) for sahara
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.6130 0.1325 0.9840 0.0623 0.1529 0.9873 0.0463 0.1346 0.0239
50 0.6085 0.1197 0.9840 0.0556 0.1393 0.9859 0.0446 0.1268 0.0165
70 0.6044 0.1129 0.9838 0.0520 0.1326 0.9851 0.0433 0.1226 0.0130
80 0.5993 0.1064 0.9835 0.0484 0.1263 0.9844 0.0416 0.1186 0.0102
90 0.5838 0.0931 0.9828 0.0407 0.1141 0.9830 0.0373 0.1103 0.0051
95 0.5534 0.0773 0.9814 0.0310 0.1008 0.9814 0.0307 0.1005 0.0001
98 0.4796 0.0561 0.9787 0.0171 0.0848 0.9791 0.0197 0.0878 0.0039
99 0.4041 0.0430 0.9763 0.0082 0.0758 0.9775 0.0121 0.0803 0.0059
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Table 2(f). The results of the Angstrom coefficients of single scattering albedo using Equation (2) for sahara model at the
respective rela tive humid itie s
RH Linear Quadratic Cubic
(%) Α α1 α2 α1 α2 α3
0 0.132502 0.062268 0.15288 0.046363 0.13473 0.023788
50 0.119753 0.055814 0.13917 0.044891 0.12671 0.016337
70 0.112727 0.051800 0.13262 0.043217 0.12283 0.012838
80 0.106435 0.048374 0.12638 0.041661 0.11872 0.01004
90 0.093124 0.040653 0.11421 0.037474 0.11059 0.004755
95 0.077282 0.030909 0.10094 0.030828 0.10085 0.000121
98 0.056080 0.017218 0.08459 0.019982 0.08774 0.00413
99 0.043050 0.008194 0.07587 0.01212 0.08035 0.00587
can be observed that they are approximately the same
with some to three places of decimal while some to four
places of decimals.
Figure 1(e) shows it is almost the opposite of Figure
1(d), and the plots can be barely approximated by power
law and it decreases with the increase in RH.
Table 2(g) shows that the correlations decrease with
the increase in RH, but increase with the increase in the
power of the polynomials.
Comparing the coefficients in Tables 2(g) and (h) it
can be observed that they are approximately the same,
some to one place of decimals while some to two places
of decimals.
Figure 2(a) shows a steep but smooth decrease of the
extinction coefficients with wavelengths and all the plots
satisfy power law.
Table 3(a) shows very good correlations for all the
polynomials, and the correlations increase with the in-
crease in the powers of the polynomials.
Figure 2(b) shows a steep but smooth curves that de-
crease with the increase in wavelength, but shows little
effect with the increase in RH. They all satisfy power
law.
Table 3(b) shows very good correlations for all the
polynomials, and the correlations increase with the in-
crease in the powers of the polynomials.
Figures 2(c) and (a) are almost similar.
Table 3(c) shows very good correlations for all the
equations, but the correlation increases with the increase
in the power of the polynomials.
From Table 3(d) it can be seen that they are approxi-
mately the same, with some to one place of decimal while
some to two places of decimals.
Figure 2(d) shows that not all can satisfy power law.
Table 3(e) shows that the correlations decrease with
the increase in RH, but increase with the increase in the
power of the polynomials.
Comparing the coefficients in Tables 3(e) and (f) it
can be observed that they are approximately the same
with some to two places of decimals while some to four
places of decimals.
Figure 2(e) is almost the inverse of Figure 2(d).
Table 3(g) shows very good correlations between, and
the correlation increases with the increase in the power of
the polynomials.
Comparing Tables 3(g) and (h), the linear part shows
that at 0%, 50% and 70% RH, they are the same to one
place of decimal places. After that they are completely
different.
Comparing Figures 3(a) and 2(a) it can be observed
that they are similar.
Table 4(a) shows very good correlations for all the
polynomials, and the correlations increase with the in-
crease in the powers of the polynomials.
From Figure 3(b), the plots barely obey power law.
Table 4(b) shows that the correlations decrease with
the increase in RH, but increase with the increase in the
power of the polynomials.
Comparing Figures 3(c) and 2(c) it can be observed
that they are similar.
Table 4(c) shows very good correlations, and the cor-
relations increases with the increase in the power of the
polynomials.
From Table 4(d) it can be seen that the coefficients
are approximately the same to one place of decimal and
some to two places of decimals.
Figure 3(d) shows that power law is not obeyed.
Table 4(e) shows that there are poor correlations in the
linear part, but the correlation improves with the increase
in the power of the polynomials.
Comparing the coefficients of Tables 4(e) and (f) it
can be observed that they are all approximately the same
within two places of decimals, while some to four places
of decimals.
Figure 3(e), is the inverse of Figure 3(d) and the
power law is not obeyed.
Table 4(g) shows that there are poor correlations in
the linear part, but the correlation improves with the in-
crease in the power of the polynomials.
Comparing the coefficients of Tables 4(g) and (h) it
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0.5 1.0 1.5 2.0 2.5
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Single Scattering Co-Albedo
Wavelengths(
m)
SSCA00 SSCA50
SSCA70 SSCA80
SSCA90 SSCA95
SSCA98 SSCA99
Figure 1(e). A graph of single scattering co-albedo against wavelength for sahara at RHs 0%, 50%, 70%, 80%, 90%, 95%,
98% and 99%.
Table 2(g). The results of the Angstrom coefficients of single scattering co-albedo using Equations (5), (6) and (10) for sahara
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.6604 0.6854 0.9563 0.3730 0.6800 0.9820 0.5976 0.9363 0.3359
50 0.6450 0.6510 0.9521 0.3451 0.6658 0.9803 0.5714 0.9240 0.3385
70 0.6342 0.6308 0.9511 0.3271 0.6610 0.9795 0.5488 0.9139 0.3315
80 0.6242 0.6101 0.9499 0.3100 0.6532 0.9787 0.5278 0.9018 0.3258
90 0.5946 0.5710 0.9481 0.2711 0.6527 0.9774 0.4818 0.8930 0.3151
95 0.5480 0.5172 0.9427 0.2183 0.6507 0.9743 0.4247 0.8863 0.3088
98 0.4483 0.4324 0.9379 0.1246 0.6699 0.9695 0.3150 0.8871 0.2848
99 0.3625 0.3721 0.9352 0.0536 0.6932 0.9654 0.2319 0.8966 0.2666
Table 2(h). The results of the Angstrom coefficients of single scattering co-albedo using Equation (3) for sahara model at the
respective rela tive humid itie s.
RH Linear Quadratic Cubic
(%) α α1 α2 α1 α2 α3
0 0.68333 0.37147 0.678817 0.59818 0.937478 0.339073
50 0.64979 0.3433 0.667123 0.56704 0.922397 0.334632
70 0.631366 0.32723 0.662004 0.54863 0.914611 0.331136
80 0.61253 0.3103 0.657862 0.52921 0.907625 0.327408
90 0.571652 0.27204 0.652168 0.48483 0.894952 0.31826
95 0.51703 0.21752 0.65193 0.42055 0.883569 0.30365
98 0.431835 0.12473 0.668464 0.31204 0.882169 0.280141
99 0.370726 0.0523 0.693104 0.22958 0.895362 0.265135
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0.5 1.0 1.52.0 2.5
0.0
0.5
1.0
1.5
2.0
Scattering Coefficients(km
-1
)
Wavelengths(
m)
SCATCO00
SCATCO50
SCATCO70
SCATCO80
SCATCO90
SCATCO95
SCATCO98
SCATCO99
Figure 2(a). A graph of scattering coefficients against wavelength for urban at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
Table 3(a). The results of the Angstrom coefficients of scattering coefficients using Equations (5), (6) and (10) for urban
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.9906 1.5018 0.9961 1.5781 0.1661 0.9993 1.7201 0.0041 0.2124
50 0.9853 1.5793 0.9986 1.7040 0.2714 0.9997 1.7925 0.1704 0.1324
70 0.9816 1.5962 0.9992 1.7416 0.3165 0.9998 1.8045 0.2447 0.0941
80 0.9779 1.6022 0.9995 1.7647 0.3537 0.9998 1.8060 0.3065 0.0618
90 0.9698 1.5917 0.9997 1.7820 0.4143 0.9997 1.7851 0.4107 0.0047
95 0.9602 1.5506 0.9995 1.7641 0.4648 0.9996 1.7325 0.5008 0.0473
98 0.9469 1.4597 0.9988 1.6925 0.5067 0.9995 1.6291 0.5791 0.0948
99 0.9373 1.3840 0.9983 1.6243 0.5231 0.9993 1.5473 0.6109 0.1151
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Absorption Coefficients (km
-1
)
Wavelength(
m)
ABSCO00
ABSCO50
ABSCO70
ABSCO80
ABSCO90
ABSCO95
ABSCO98
ABSCO99
Figure 2(b). A graph of absorption coefficients against wavelength for urban at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
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Table 3(b). The results of the Angstrom coefficients of absorption coefficients using Equations (5), (6) and (10) for urban
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.9958 1.0326 0.9971 1.0072 0.0554 0.9989 0.9344 0.0277 0.1089
50 0.9951 1.0269 0.9967 0.9984 0.0620 0.9988 0.9207 0.0267 0.1163
70 0.9948 1.0242 0.9966 0.9941 0.0655 0.9987 0.9156 0.0241 0.1174
80 0.9945 1.0216 0.9966 0.9900 0.0688 0.9987 0.9112 0.0211 0.1178
90 0.9940 1.0157 0.9965 0.9806 0.0763 0.9986 0.9029 0.0123 0.1162
95 0.9932 1.0067 0.9966 0.9664 0.0877 0.9986 0.8925 0.0034 0.1105
98 0.9914 0.9889 0.9970 0.9385 0.1097 0.9984 0.8756 0.0380 0.0940
99 0.9892 0.9716 0.9973 0.9117 0.1304 0.9982 0.8618 0.0734 0.0746
0.51.01.52.02.5
0.0
0.5
1.0
1.5
2.0
2.5
Extinction Coefficients(km
-1
)
Wavelengths(
m)
EXTCO00
EXTCO50
EXTCO70
EXTCO80
EXTCO90
EXTCO95
EXTCO98
EXTCO99
Figure 2(c). A graph of extinction coefficients against wavelength for urban at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
Table 3(c). The results of the Angstrom coefficients of extinction coefficients using Equations (5), (6) and (10) for urban
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.9975 1.3058 0.9985 1.3332 0.0597 0.9995 1.4040 0.0210 0.1058
50 0.9946 1.3899 0.9991 1.4535 0.1384 0.9998 1.5150 0.0682 0.0920
70 0.9921 1.4196 0.9993 1.5021 0.1795 0.9998 1.5555 0.1185 0.0800
80 0.9893 1.4403 0.9995 1.5402 0.2176 0.9999 1.5843 0.1674 0.0659
90 0.9824 1.4620 0.9998 1.5947 0.2889 0.9999 1.6166 0.2640 0.0327
95 0.9728 1.4572 0.9999 1.6229 0.3607 0.9999 1.6168 0.3676 0.0090
98 0.9579 1.4055 0.9995 1.6049 0.4340 0.9998 1.5647 0.4799 0.0601
99 0.9472 1.3480 0.9990 1.5627 0.4673 0.9996 1.5047 0.5335 0.0868
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Table 3(d). The results of the Angstrom coefficients of extinction coefficients using Equations (1), (7), (9) and (12) for urban
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) Equation (7) Equation (1) Equation (9) Equation (1) Equation (12) Equation (1)
α α α1(λ) α1(λ) α2(λ) α2(λ)
0 1.305762 1.317118 1.296971 1.285558 1.260416 1.267717
50 1.389882 1.408679 1.369510 1.351385 1.337729 1.344704
70 1.419598 1.440412 1.393177 1.372674 1.365554 1.371538
80 1.440264 1.462055 1.408237 1.386470 1.385480 1.390167
90 1.461972 1.483500 1.419447 1.397601 1.408146 1.410535
95 1.457184 1.475636 1.404097 1.384973 1.407222 1.407436
98 1.405514 1.418383 1.341632 1.328506 1.362398 1.361215
99 1.348026 1.357473 1.279248 1.269739 1.309238 1.307432
0.51.01.52.02.5
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Single Scattering Albedo
Wavelengths(
m)
SSA00 SSA50
SSA70 SSA80
SSA90 SSA95
SSA98 SSA99
Figure 2(d). A graph of single scattering albedo against wavelength for urban at RHs 0%, 50%, 70%, 80%, 90%, 95%, 98%
and 99%.
Table 3(e). The results of the Angstrom coefficients of single scattering albedo using Equations (5), (6) and (10) for urban
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.8376 0.1961 0.9498 0.2450 0.1064 0.9898 0.3162 0.0252 0.1064
50 0.8070 0.1893 0.9884 0.2505 0.1331 0.9942 0.2772 0.1026 0.0400
70 0.7798 0.1766 0.9933 0.2396 0.1370 0.9942 0.2491 0.1261 0.0143
80 0.7515 0.1620 0.9931 0.2246 0.1362 0.9932 0.2216 0.1396 0.0044
90 0.6908 0.1297 0.9836 0.1872 0.1252 0.9890 0.1682 0.1469 0.0285
95 0.6169 0.0935 0.9637 0.1412 0.1039 0.9806 0.1155 0.1331 0.0384
98 0.5108 0.0542 0.9320 0.0877 0.0729 0.9656 0.0646 0.0993 0.0345
99 0.4347 0.0359 0.9104 0.0615 0.0557 0.9540 0.0426 0.0772 0.0283
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Table 3(f). The results of the Angstrom coefficients of single scattering albedo using Equation (2) for urban model at the re-
spective relative humidities.
RH Linear Quadratic Cubic
(%) α α1 α2 α1 α2 α3
0 0.196057 0.244939 0.106400 0.316179 0.025120 0.106549
50 0.189424 0.250513 0.132973 0.277519 0.102162 0.040390
70 0.176572 0.239505 0.136985 0.248942 0.126217 0.014115
80 0.161910 0.224417 0.136057 0.221713 0.139142 0.004044
90 0.129716 0.187304 0.125352 0.168540 0.146761 0.028065
95 0.093392 0.141213 0.104091 0.115660 0.133245 0.038218
98 0.054221 0.087622 0.072703 0.064399 0.099199 0.034733
99 0.035931 0.061562 0.055790 0.042615 0.077408 0.028338
0.5 1.0 1.5 2.02.5
0.1
0.2
0.3
0.4
0.5
0.6
Single Scattering Co-Albedo
Wavelengths(
m)
SSCA00
SSCA50
SSCA70
SSCA80
SSCA90
SSCA95
SSCA98
SSCA99
Figure 2(e). A graph of single scattering co-albedo against wavelength for urban at RHs 0%, 50%, 70%, 80%, 90%, 95%,
98% and 99%.
Table 3(g). The results of the Angstrom coefficients of single scattering co-albedo using Equations (5), (6) and (10) for urban
model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.8636 0.2906 0.8981 0.5267 0.0928 0.9096 0.1643 0.2374 0.0831
50 0.9171 0.3964 0.9780 0.5457 0.0587 0.9425 0.0459 0.4805 0.1357
70 0.9291 0.4395 0.9313 0.5270 0.0344 0.9508 0.1609 0.5924 0.1577
80 0.9327 0.4714 0.9327 0.4762 0.0019 0.9548 0.3073 0.7121 0.1796
90 0.9258 0.5157 0.9320 0.3446 0.0673 0.9585 0.5964 0.9248 0.2158
95 0.8984 0.5383 0.9292 0.1331 0.1593 0.9593 0.9312 1.1292 0.2440
98 0.8247 0.5262 0.9197 0.1593 0.2855 0.9562 1.3954 1.3749 0.2741
99 0.7478 0.4986 0.9077 0.2855 0.0695 0.9510 1.7342 1.5489 0.2970
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Table 3(h). The results of the Angstrom coefficients of single scattering co-albedo using Equation (3) for urban model at the
respective rela tive humid itie s.
RH Linear Quadratic Cubic
(%) α α1 α2 α1 α2 α3
0 0.273154 0.326035 0.115104 0.469589 0.048684 0.214705
50 0.362993 0.455074 0.200432 0.594301 0.041582 0.208233
70 0.395439 0.508002 0.245014 0.639970 0.094445 0.197376
80 0.418647 0.550228 0.286412 0.673048 0.146282 0.183694
90 0.446297 0.614085 0.365224 0.713632 0.251647 0.148885
95 0.450505 0.656495 0.448377 0.724332 0.370979 0.101459
98 0.416653 0.666450 0.543730 0.689108 0.517878 0.033888
99 0.376471 0.651039 0.597649 0.642886 0.606951 0.012194
0.5 1.0 1.5 2.0 2.5
0.00
0.05
0.10
0.15
0.20
Scattering Coefficients(km
-1
)
Wavelengths(
m)
SCATCO00
SCATCO50
SCATCO70
SCATCO80
SCATCO90
SCATCO95
SCATCO98
SCATCO99
Figure 3(a). A graph of scattering coefficients against wavelength for continental clean at RHs 0%, 50%, 70%, 80%, 90%,
95%, 98% and 99%.
Table 4(a). The results of the Angstrom coefficients of scattering coefficients using Equations (5), (6) and (10) for continental
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.9887 1.3858 0.9956 1.4647 0.1718 0.9991 1.6016 0.0156 0.2048
50 0.9839 1.5029 0.9985 1.6276 0.2715 0.9997 1.7142 0.1727 0.1295
70 0.9802 1.5327 0.9992 1.6781 0.3164 0.9998 1.7403 0.2454 0.0931
80 0.9763 1.5483 0.9995 1.7108 0.3537 0.9998 1.7522 0.3065 0.0619
90 0.9682 1.5522 0.9998 1.7429 0.4151 0.9998 1.7469 0.4106 0.0060
95 0.9586 1.5227 0.9995 1.7371 0.4666 0.9997 1.7067 0.5013 0.0455
98 0.9451 1.4423 0.9988 1.6764 0.5096 0.9995 1.6141 0.5807 0.0933
99 0.9356 1.3710 0.9983 1.6127 0.5260 0.9993 1.5366 0.6129 0.1138
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0.5 1.0 1.52.0 2.5
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Absorption Coefficients(km
-1
)
Wavelengths(
m)
ABSCO00 ABSCO50
ABSCO70 ABSCO80
ABSCO90 ABSCO95
ABSCO98 ABSCO99
Figure 3(b). A graph of absorption coefficients against wavelength for continental clean at RHs 0%, 50%, 70%, 80%, 90%,
95%, 98% and 99%.
Table 4(b). The results of the Angstrom coefficients of absorption coefficients using Equations (5), (6) and (10) for continental
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.7321 0.8145 0.7574 0.7114 0.2243 0.9472 0.0227 0.5615 1.0300
50 0.6988 0.7801 0.7326 0.6633 0.2542 0.9397 0.0419 0.5504 1.0547
70 0.6866 0.7655 0.7252 0.6419 0.2690 0.9368 0.0638 0.5362 1.0555
80 0.6757 0.7518 0.7195 0.6214 0.2838 0.9343 0.0824 0.5193 1.0527
90 0.6537 0.7228 0.7108 0.5773 0.3168 0.9293 0.1166 0.4749 1.0378
95 0.6226 0.6824 0.7026 0.5158 0.3626 0.9219 0.1567 0.4047 1.0058
98 0.5596 0.6126 0.6940 0.4082 0.4450 0.9083 0.2214 0.2733 0.9416
99 0.4973 0.5532 0.6912 0.3180 0.5120 0.8954 0.2707 0.1597 0.8805
0.5 1.0 1.5 2.0 2.5
0.00
0.05
0.10
0.15
0.20
Extinction Coefficients(km
-1
)
Wavelengths(
m)
EXTCO00
EXTCO50
EXTCO70
EXTCO80
EXTCO90
EXTCO95
EXTCO98
EXTCO99
Figure 3(c). A graph of extinction coefficients against wavelength for continental clean at RHs 0%, 50%, 70%, 80%, 90%,
95%, 98% and 99%.
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Table 4(c). The results of the Angstrom coefficients of extinction coefficients using Equations (5), (6) and (10) for continental
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.9951 1.3264 0.9988 1.3815 0.1200 0.9993 1.4324 0.0620 0.0761
50 0.9891 1.4450 0.9995 1.5460 0.2197 0.9997 1.5823 0.1782 0.0544
70 0.9852 1.4790 0.9997 1.6010 0.2655 0.9998 1.6265 0.2364 0.0381
80 0.9813 1.4991 0.9998 1.6390 0.3046 0.9998 1.6529 0.2888 0.0207
90 0.9732 1.5122 0.9998 1.6827 0.3711 0.9999 1.6729 0.3822 0.0146
95 0.9633 1.4924 0.9996 1.6898 0.4295 0.9998 1.6551 0.4691 0.0518
98 0.9495 1.4220 0.9991 1.6432 0.4816 0.9997 1.5828 0.5505 0.0903
99 0.9397 1.3554 0.9986 1.5864 0.5028 0.9995 1.5140 0.5853 0.1082
Table 4(d). The results of the Angstrom coefficients of extinction coefficients using Equations (1), (7), (9) and (12) for conti-
nental clean model at the respe c t ive relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) Equation (7) Equation (1) Equation (9) Equation (1) Equation (12) Equation (1)
α α α1(λ) α1(λ) α2(λ) α2(λ)
0 1.326374 1.323762 1.308708 1.288183 1.282407 1.297761
50 1.445043 1.446130 1.412712 1.390209 1.393925 1.411310
70 1.478996 1.481190 1.439914 1.417335 1.426736 1.443978
80 1.499053 1.501993 1.454219 1.432156 1.447062 1.463395
90 1.512202 1.515944 1.457587 1.437578 1.462620 1.476845
95 1.492423 1.496337 1.429202 1.412395 1.447108 1.458491
98 1.421950 1.425678 1.351065 1.338642 1.382278 1.390248
99 1.355396 1.358777 1.281397 1.271155 1.318791 1.324581
0.51.01.52.02.5
0.80
0.85
0.90
0.95
1.00
Single Scattering Albedo
Wavelengths(
m)
SSA00 SSA50
SSA70 SSA80
SSA90 SSA95
SSA98 SSA99
Figure 3(d). A graph of single scattering albedo against wavelength for continental clean at RHs 0%, 50%, 70%, 80%, 90%,
95%, 98% and 99%.
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Table 4(e). The results of the Angstrom coefficients of single scattering albedousing Equations (5), (6) and (10) for continental
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.4258 0.0592 0.5733 0.0830 0.0517 0.8994 0.1691 0.0465 0.1288
50 0.5636 0.0578 0.7714 0.0817 0.0520 0.9251 0.1318 0.0052 0.0749
70 0.5886 0.0537 0.8283 0.0771 0.0508 0.9299 0.1142 0.0085 0.0555
80 0.5963 0.0493 0.8647 0.0718 0.0490 0.9317 0.0992 0.0177 0.0410
90 0.5850 0.0400 0.9057 0.0602 0.0439 0.9300 0.0737 0.0285 0.0202
95 0.5456 0.0303 0.9168 0.0472 0.0370 0.9205 0.0514 0.0323 0.0062
98 0.4788 0.0202 0.9037 0.0331 0.0281 0.9053 0.0311 0.0303 0.0029
99 0.4350 0.0155 0.8847 0.0262 0.0233 0.8939 0.0224 0.0276 0.0056
Table 4(f). The results of the Angstrom coefficients of single scattering albedo using Equations (2) for continental clean model
at the respective relative humidities.
RH Linear Quadratic Cubic
(%) α α1 α2 α1 α2 α3
0 0.059431 0.083205 0.051747 0.169206 0.046376 0.128627
50 0.057803 0.081609 0.051818 0.131833 0.005485 0.075117
70 0.053680 0.077069 0.050912 0.113828 0.008971 0.054979
80 0.049226 0.071792 0.049118 0.099330 0.017699 0.041187
90 0.039996 0.060241 0.044067 0.073978 0.028393 0.020547
95 0.030288 0.047315 0.037062 0.051545 0.032235 0.006327
98 0.020366 0.033218 0.027974 0.031264 0.030203 0.002922
99 0.015601 0.026296 0.023278 0.022555 0.027546 0.005594
0.51.01.52.02.
5
0.00
0.05
0.10
0.15
0.20
Single Scattering Co-Albedo
Wavelengths(
m)
SSCA00
SSCA50
SSCA70
SSCA80
SSCA90
SSCA95
SSCA98
SSCA99
Figure 3(e). A graph of single scattering co-albedo against wavelength for continental clean at RHs 0%, 50%, 70%, 80%,
90%, 95%, 98% and 99%.
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Table 4(g). The results of the Angstrom coefficients of single scattering co-albedo using Equations (5), (6) and (10) for conti-
nental clean model at the respect ive re lative humidities using regression anal ysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.4639 0.5115 0.5585 0.6689 0.3425 0.9093 1.4075 0.5003 1.1048
50 0.5534 0.6649 0.6829 0.8839 0.4767 0.9333 1.6267 0.3708 1.1109
70 0.5742 0.7143 0.7200 0.9595 0.5337 0.9386 1.6912 0.3012 1.0944
80 0.5820 0.7472 0.7475 1.0186 0.5907 0.9425 1.7369 0.2289 1.0743
90 0.5831 0.7899 0.7850 1.1065 0.6890 0.9438 1.7909 0.0918 1.0236
95 0.5671 0.8087 0.8147 1.1726 0.7921 0.9433 1.8121 0.0625 0.9564
98 0.5308 0.8104 0.8471 1.2365 0.9275 0.9419 1.8051 0.2788 0.8504
99 0.5013 0.8068 0.8635 1.2738 1.0165 0.9396 1.7958 0.4209 0.7808
Table 4(h). The results of the Angstrom coefficients of single scattering co-albedo using Equation (3) for continental clean
model at the respective relative humidities.
RH Linear Quadratic Cubic
(%) α α1 α2 α1 α2 α3
0 0.511894 0.670076 0.344312 1.409672 0.499528 1.106169
50 0.664984 0.882661 0.473817 1.624198 0.372238 1.109071
70 0.713497 0.959074 0.534546 1.690289 0.299732 1.093633
80 0.747241 1.017557 0.588393 1.735258 0.230466 1.073422
90 0.789407 1.105397 0.687812 1.789529 0.092746 1.023214
95 0.810037 1.173939 0.792101 1.811768 0.064371 0.953962
98 0.809353 1.235052 0.926614 1.804207 0.277238 0.851250
99 0.802192 1.268369 1.014724 1.784694 0.425625 0.772235
can be observed that they are approximately the same
within two places of decimals, with some to three places
of decimals.
Figure 4(a) shows that power law decreases with the
increase in RHs.
From Table 5(a), it can be observe that the correla-
tions decrease with the increase in RHs, but increases
with the increase in the power of the polynomials.
From Figure 4(b) it can be observed that power law is
not obeyed.
Table 5(b) shows poor correlation in the linear part,
but good correlations at second and third order polyno-
mials, and the correlations increase with the increase in
order of the polynomials and RHs.
Comparing Figures 4(c) and (a), it can be observed
that they are similar.
From Table 5(c), it can be seen that the correlations
decrease with the increase in RHs, but increases with the
increase in the power of the polynomials.
From Table 5(d), from the linear part it can be seen
that Equation (1) underestimated Equation (7) at 0% to
70% RH, and overestimated it at 90% to 99% RH. At the
quadratic part Equations (1) and (9) are equal within two
places of decimals, but at RHs 95% to 99% Equation (1)
underestimated Equation (9). At the cubic part, Equations
(1) and (12) are the same within two places of decimals
except at 98% and 99% where Equation (1) underesti-
mated Equation (2).
Figure 4(d) shows that power law is not obeyed.
From Table 5(e) it can be seen from the linear part
that there is a poor correlation between single scattering
albedo and wavelength, though as the power of the poly-
nomials increase the relation also improves.
Comparing Tables 5(e) and (f) it can be observed that
in the linear part only the values at 80%, 95% and 99%
agree to three places of decimals. This can be attributed
to the poor correlations at Table 5(e). From the quadratic
and cubic some coefficients agree to two places while
some to three places of decimals.
Figure 4(e) in the inverse of Figure 4( d).
Table 5(g) shows poor correlations in the linear part.
There are good correlations at quadratic and cubic poly-
nomials, though poor correlation can be observed at 99%
RH throughout.
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0.51.01.52.02.5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Scattering Coefficients(km
-1
)
Wavelengths(
m)
SCATCO00 SCATCO50
SCATCO70 SCATCO80
SCATCO90 SCATCO95
SCATCO98 SCATCO99
Figure 4(a). A graph of scattering coefficients against wavelength for maritime clean at RHs 0%, 50%, 70%, 80%, 90%, 95%,
98% and 99%.
Table 5(a). The results of the Angstrom coefficients of scattering coefficients using Equations (5), (6) and (10) for maritime
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.8698 0.5242 0.9906 0.6572 0.2896 0.9989 0.5721 0.3867 0.1273
50 0.7704 0.3328 0.9539 0.4434 0.2408 0.9946 0.3163 0.3858 0.1901
70 0.7525 0.2866 0.9366 0.3832 0.2102 0.9915 0.2546 0.3568 0.1922
80 0.7397 0.2515 0.9199 0.3360 0.1841 0.9883 0.2091 0.3289 0.1899
90 0.7244 0.1908 0.8796 0.2510 0.1310 0.9784 0.1340 0.2645 0.1750
95 0.7060 0.1340 0.8192 0.1706 0.0796 0.9554 0.0728 0.1911 0.1462
98 0.6908 0.0730 0.7125 0.0818 0.0192 0.8845 0.0213 0.0882 0.0905
99 0.6084 0.0401 0.6268 0.0353 0.0103 0.7891 9.5139 0.0289 0.0514
0.51.01.52.02.5
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.010
0.011
Absorption Coefficients(km
-1
)
Wavelengths(
m)
ABSCO00
ABSCO50
ABSCO70
ABSCO80
ABSCO90
ABSCO95
ABSCO98
ABSCO99
Figure 4(b). A graph of absorption coefficients against wavelength for maritime clean at RHs 0%, 50%, 70%, 80%, 90%,
95%, 98% and 99%.
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Table 5(b). The results of the Angstrom coefficients of absorption coefficients using Equations (5), (6) and (10) for maritime
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.2846 0.4908 0.6576 0.1081 0.8328 0.8516 0.5647 0.0652 1.0063
50 0.0391 0.1833 0.7554 0.3512 1.1634 0.8894 0.9147 0.5204 0.8429
70 0.0067 0.0799 0.7822 0.5037 1.2703 0.8899 1.0339 0.6653 0.7930
80 0.0001 0.0106 0.8041 0.6368 1.3629 0.8903 1.1369 0.7923 0.7480
90 0.0277 0.1927 0.8392 0.9028 1.5455 0.8943 1.3540 1.0307 0.6748
95 0.0961 0.4180 0.8720 1.2267 1.7603 0.9050 1.6339 1.2957 0.6090
98 0.2118 0.7747 0.9045 1.7287 2.0765 0.9230 2.1088 1.6428 0.5686
99 0.2933 1.0722 0.9205 2.1399 2.3242 0.9338 2.5189 1.8917 0.5669
0.51.01.52.02.5
0.0
0.1
0.2
0.3
0.4
0.5
Extinction Coefficients(km
-1
)
Wavelengths(
m)
EXTCO00 EXTCO50
EXTCO70 EXTCO80
EXTCO90 EXTCO95
EXTCO98 EXTCO99
Figure 4(c). A graph of extinction coefficients against wavelength for maritime clean at RHs 0%, 50%, 70%, 80%, 90%, 95%,
98% and 99%.
Table 5(c). The results of the Angstrom coefficients of extinction coefficients using Equations (5), (6) and (10) for maritime
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.8883 0.5272 0.9880 0.6475 0.2618 0.9998 0.5464 0.3772 0.1512
50 0.7887 0.3333 0.9515 0.4365 0.2245 0.9966 0.3041 0.3755 0.1980
70 0.7704 0.2863 0.9352 0.3765 0.1963 0.9942 0.2449 0.3464 0.1968
80 0.7571 0.2501 0.9180 0.3286 0.1709 0.9910 0.1997 0.3180 0.1928
90 0.7395 0.1877 0.8798 0.2434 0.1212 0.9817 0.1277 0.2533 0.1731
95 0.7260 0.1300 0.8153 0.1611 0.0676 0.9608 0.0644 0.1778 0.1445
98 0.7056 0.0686 0.7108 0.0726 0.0088 0.8872 0.0157 0.0737 0.0852
99 0.5279 0.0332 0.6218 0.0236 0.0207 0.7764 0.0062 0.0133 0.0446
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Table 5(d). The results of the Angstrom coefficients of extinction coefficients using Equations (1), (7), (9) and (12) for mari-
time clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) Equation (7) Equation (1) Equation (9) Equation (1) Equation (12) Equation (1)
α α α1(λ) α1(λ) α2(λ) α2(λ)
0 0.527214 0.508211 0.488677 0.486895 0.540925 0.548030
50 0.333319 0.328780 0.300276 0.298072 0.368672 0.371082
70 0.286304 0.284118 0.257418 0.254929 0.325406 0.327440
80 0.250051 0.250105 0.224894 0.222541 0.291486 0.293302
90 0.187726 0.190850 0.169883 0.167824 0.229678 0.232161
95 0.130000 0.135132 0.120053 0.115855 0.169988 0.169726
98 0.068600 0.075620 0.067313 0.059593 0.096742 0.094223
99 0.033156 0.043773 0.036207 0.026458 0.051601 0.048180
0.51.01.52.02.5
0.92
0.94
0.96
0.98
1.00
Single Scattering Albedo
Wavelengths(
m)
SSA00 SSA50
SSA70 SSA80
SSA90 SSA95
SSA98 SSA99
Figure 4(d). A graph of single scattering albedo against wavelength for maritime clean at RHs 0%, 50%, 70%, 80%, 90%,
95%, 98% and 99%.
Table 5(e). The results of the Angstrom coefficients of single scattering albedo using Equations (4), (5) and (6) for maritime
clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Quadratic Cubic
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.0260 0.0039 0.5943 0.0085 0.0271 0.7281 0.0233 0.0103 0.0220
50 0.0004 0.0003 0.6761 0.0071 0.0159 0.7296 0.0121 0.0102 0.0075
70 0.0035 0.0007 0.7124 0.0073 0.0144 0.7396 0.0105 0.0108 0.0047
80 0.0165 0.0013 0.7493 0.0074 0.0133 0.7614 0.0093 0.0111 0.0029
90 0.0684 0.0023 0.7647 0.0074 0.0110 0.7650 0.0071 0.0113 0.0004
95 0.1733 0.0036 0.8283 0.0085 0.0105 0.8358 0.0072 0.0119 0.0019
98 0.2977 0.0052 0.8145 0.0098 0.0101 0.8683 0.0062 0.0143 0.0055
99 0.3691 0.0068 0.8278 0.0119 0.0112 0.8850 0.0075 0.0162 0.0066
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Table 5(f). The results of the Angstrom coefficients of single scattering albedo using equations (2) for maritime clean model at
the respective relative humidities.
RH Linear Quadratic Cubic
(%) α α1 α2 α1 α2 α3
0 0.003031 0.009733 0.027784 0.025744 0.009515 0.023948
50 0.000519 0.006946 0.016250 0.012226 0.010226 0.007896
70 0.000302 0.006685 0.013895 0.009724 0.010429 0.004544
80 0.001435 0.007465 0.013124 0.009357 0.010965 0.002831
90 0.003115 0.007588 0.009736 0.006272 0.011237 0.001968
95 0.003996 0.009503 0.011988 0.008400 0.013246 0.001649
98 0.004397 0.009176 0.010401 0.005641 0.014434 0.005286
99 0.006924 0.011701 0.010399 0.007112 0.015636 0.006865
0.5 1.0 1.5 2.0 2.5
0.00
0.02
0.04
0.06
0.08
Single Scattering Co-Albedo
Wavelengths(
m)
SSCA00
SSCA50
SSCA70
SSCA80
SSCA90
SSCA95
SSCA98
SSCA99
Figure 4(e). A graph of single scattering co-albedo against wavelength for maritime clean at RHs 0%, 50%, 70%, 80%, 90%,
95%, 98% and 99%.
Table 5(g). The results of the Angstrom coefficients of single scattering co-albedo using Equations (5), (6) and (10) for mari-
time clean model at the respective relative humidities using regression analysis with SPSS16.0.
RH Linear Equation (5) Quadratic Equation (6) Cubic Equation (10)
(%) R2 α R
2 α1 α2 R
2 α1 α2 α3
0 0.0012 0.0302 0.7001 0.5346 1.0978 0.8425 1.0898 0.4644 0.8304
50 0.0257 0.1670 0.8072 0.7943 1.3654 0.8798 1.2605 0.8335 0.6973
70 0.0417 0.2199 0.8484 0.8785 1.4336 0.8947 1.2634 0.9944 0.5757
80 0.0575 0.2906 0.8604 1.0301 1.6097 0.9018 1.4397 1.1424 0.6126
90 0.0964 0.3763 0.8397 1.0881 1.5493 0.8530 1.3202 1.2845 0.3472
95 0.1709 0.6389 0.8835 1.5274 1.9340 0.9221 2.0316 1.3586 0.7542
98 0.2308 0.7704 0.8858 1.6544 1.9240 0.8870 1.7469 1.8184 0.1384
99 0.1270 0.5957 0.2027 0.9088 0.6816 0.3329 0.0929 1.8245 1.4982
Comparing Tables 5(g) and (h) it can be seen that
from the linear part they are different, and this can be
attributed to the poor correlations in 5(g). From the quad-
ratic and cubic, the coefficients from Tables 5(g) and (h)
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Table 5(h). The results of the Angstrom coefficients of single scattering co-albedo using Equation (3) for maritime clean
model at the respective relative humidities.
RH Linear Quadratic Cubic
(%) α α1 α2 α1 α2 α3
0 0.036462 0.539358 1.094649 0.018294 0.312034 1.157534
50 0.150011 0.787625 1.387888 0.610640 0.144866 1.040860
70 0.206397 0.880150 1.466550 0.789011 0.318965 0.989806
80 0.260667 0.965345 1.533866 0.937193 0.474357 0.940760
90 0.380442 1.146174 1.666761 1.226255 0.777471 0.847912
95 0.548017 1.387765 1.827872 1.569516 1.117854 0.753569
98 0.843281 1.801288 2.085286 2.093174 1.569053 0.653780
99 1.105303 2.163529 2.303430 2.525064 1.878473 0.611415
are almost the same, but to only one place of decimals.
4. Conclusions
From all the tables and graphs obtained, it can be seen
that it is only urban aerosols that scattering, absorption
and extinction coefficients that satisfy power laws excel-
lently at this spectral range and can be seen that it is the
only aerosols that show very good relations between the
estimated Equations (1)-(3) and the linear Equation (5).
Linear models are considered most important, because
they are the values that are obtainable from remote sens-
ing and ground truthing instruments.
Another observation made is that Equations (1) and (2)
are sufficient. This is because the information that can be
obtained from equation is almost the same as that of
Equation (3).
Additional important observation made from the vari-
ous graphs is that, at the spectral range of 0.4 to 1.5
power laws are obeyed by all the aerosols. Therefore,
since 99% of sun’s radiation falls between 0.2 - 5.6 μm;
and 80% falls between 0.4 - 1.5 μm (visible and near
infrared) and the atmosphere is quite transparent to in-
coming solar radiation with the maximum radiation at
0.48 μm (visible) and in the study of the earth’s surface,
most of the remote sensing instruments are designed to
operate within solar spectral window (0.4 - 0.7 μm) and
near infrared (0.7 - 1.5 μm), where cloudless atmosphere
will transmit sufficient radiation for detection, which also
shows that these formulas can be useful in remote sens-
ing.
REFERENCES
[1] A. Angstrom, “On the Atmospheric Transmission of Sun
Radiation and on Dust in the Air,” Geografiska Annaler,
Vol. 11, 1929, pp. 156-166.
http://dx.doi.org/10.2307/519399
[2] A. Angstrom, “On the Atmospheric Transmission of Sun
Radiation II,” Geografiska Annaler, Vol. 12, 1930, pp.
130-159. http://dx.doi.org/10.2307/519561
[3] A. Angstrom, “Techniques of Determining the Turbidity
of the Atmosphere,” Tellus, Vol. 13, No. 2, 1961, pp.
214-223.
http://dx.doi.org/10.1111/j.2153-3490.1961.tb00078.x
[4] A. Angstrom, “The Parameters of Atmospheric Turbid-
ity,” Tellus, Vol. 16, No. 1, 1964, pp. 64-75.
http://dx.doi.org/10.1111/j.2153-3490.1964.tb00144.x
[5] P. B. Russell, R. W. Bergstrom, Y. Shinozuka, A. D.
Clarke, P. F. De-Carlo, J. L. Jimenez, J. M. Livingston, J.
Redemann, O. Dubovik and A. Strawa, “Absorption Ang-
strom Exponent in AERONET and Related Data as an In-
dicator of Aerosol Composition,” Atmospheric Chemistry
and Physics, Vol. 10, 2010, pp. 1155-1169.
http://dx.doi.org/10.5194/acp-10-1155-2010
[6] E. V. Fischer, D. A. Jaffe, N. A. Marley, J. S. Gaffney
and A. Marchany-Rivera, “Optical Properties of Aged
Asian Aerosols Observed over the US Pacific North-
west,” Journal of Geophysical Research, Vol. 115, No.
D20, 2010. http://dx.doi.org/10.1029/2010JD013943
[7] A. Virkkula, N. C. Ahlquist, D. S. Covert, W. P. Arnott, P.
J. Sheridan, P. K. Quinn and D. J. Coffman, “Modifica-
tion, Calibration and a Field Test of an Instrument for
Measuring Light Absorption by Particles,” Aerosol Sci-
ence and Technology, Vol. 39, No. 1, 2005, pp. 68-83.
[8] B. A. Flowers, M. K. Dubey, C. Mazzoleni, E. A. Stone, J.
J. Schauer, S.-W. Kim and S. C. Yoon, “Optical-Chemi-
cal-Microphysical Relationships and Closure Studies for
Mixed Car-Bonaceous Aerosols Observed at Jeju Island;
3-Laser Photoa-Coustic Spectrometer, Particle Sizing,
and Filter Analysis,” Atmospheric Chemistry and Physics,
Vol. 10, 2010, pp. 10387-10398.
http://dx.doi.org/10.5194/acp-10-10387-2010
[9] N. O’Neill and A. Royer, “Extraction of Bimodal Aero-
sol-Size Distribution Radii from Spectral and Angular
Slope (Angstrom) Coefficients,” Applied Optics, Vol. 32,
No. 9, 1993, pp. 1642-1645.
http://dx.doi.org/10.1364/AO.32.001642
[10] M. K. Latha and K. V. S. Badarinath, “Factors Influenc-
ing Aerosol Characteristics over Urban Environment,”
Environmental Monitoring and Assessment, Vol. 104, No.
1-3, 2005, pp. 269-280.
http://dx.doi.org/10.1007/s10661-005-1615-7
[11] J. S. Reid, T. F. Eck, S. A. Christopher, P. V. Hobbs and
B. Holben, “Use of the Angstrom Exponent to Estimate
B. I. TIJJANI ET AL.
Open Access OJAppS
512
the Variability of Optical and Physical Properties of Ag-
ing Smoke Particles in Brazil,” Journal of Geophysical
Research, Vol. 104, No. D22, 1999, pp. 27473-27489.
http://dx.doi.org/10.1029/1999JD900833
[12] T. F. Eck, B. N. Holben, D. E. Ward, M. M. Mukelabai,
O. Dubovik, A. Smirnov, J. S. Schafer, N. C. Hsu, S. J.
Piketh, A. Queface, J. Le Roux, R. J. Swap and I. Slutsker,
“Variability of Biomass Burning Aerosol Optical Char-
acteristics in Southern Africa during the SAFARI 2000
Dry Season Campaign and a Comparison of Single Scat-
tering Albedo Estimates from Radiometric Measure-
ments,” Journal of Geophysical Research, Vol. 108 No.
D13, 2003, p. 8477.
[13] T. F. Eck, B. N. Holben, J. S. Reid, O. Dubovic, A. Smir-
nov, N. T. O’Neill, I. Slutsker and S. Kinne, “Wavelength
Dependence of the Optical Depth of Biomass Burning,
Urban, and Desert Dust Aerosols,” Journal of Geophysi-
cal Research, Vol. 104, No. D24, 1999, pp. 31333-31349.
http://dx.doi.org/10.1029/1999JD900923
[14] A. Smirnov, A. Royer, N. T. O’Neill and A. Tarussov, “A
Study of the Link between Synoptic Air Mass Type and
Atmospheric Optical Parameters,” Journal of Geophysi-
cal Research, Vol. 99, No. D10, 1994, pp. 20967-20982.
http://dx.doi.org/10.1029/94JD01719
[15] N. C. Hsu, S. C. Tsay, M. D. King and J. R. Herman,
“Deep-Blue retrievals of Asian aerosol properties during
ACE-Asia,” IEEE Transactions on Geoscience and Re-
mote Sensing, Vol. 44, No. 11, 2006, pp. 3180-3195.
http://dx.doi.org/10.1109/TGRS.2006.879540
[16] H. Moosmuller, R. K. Chakrabarty and W. P. Arnott,
“Aerosol Light Absorption and Its Measurement: A Re-
view,” Journal of Quantitative Spectroscopy and Radia-
tive Transfer, Vol. 110, NO. 11, 2009, pp. 844-878.
http://dx.doi.org/10.1016/j.jqsrt.2009.02.035
[17] H. Moosmuller and R. K. Chakrabarty, “Technical Note:
Simple Analytical Relationships between Angstrom Co-
efficients of Aerosol Extinction, Scattering, Absorption,
and Single Scattering Albedo,” Atmospheric Chemistry
and Physics, Vol. 11, 2011, pp. 10677-10680.
http://dx.doi.org/10.5194/acp-11-10677-2011
[18] K. Lewis, W. P. Arnott, H. Moosmuller and C. E. Wold,
“Strong Spectral Variation of Biomass Smoke Light Ab-
sorption and Single Scattering Albedo Observed with a
Novel Dual-Wavelength Photoacoustic Instrument,” Jour-
nal of Geophysical Research, Vol. 113, No. D16, 2008.
http://dx.doi.org/10.1029/2007JD009699
[19] O. Dubovik, B. N. Holben, Y. J. Kaufman, M. Yamasoe,
A. Smirnov, D. Tanre and I. Slutsker, “Single-Scattering
Albedo of Smoke Retrieved from the Sky Radiance and
Solar Transmittance Measured from Ground,” Journal of
Geophysical Research, Vol. 103, No. D24, 1998, pp.
31901-31923. http://dx.doi.org/10.1029/98JD02276
[20] O. Dubovik and M. D. King, “A Flexible Inversion Algo-
rithm for Retrieval of Aerosol Optical Properties from
Sun and Sky Radiance Measurements,” Journal of Geo-
physical Research, Vol. 105, No. D16, 2000, pp. 20673-
20696. http://dx.doi.org/10.1029/2000JD900282
[21] M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B.
A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B.
Maring and L. D. Travis, “Accurate Monitoring of Ter-
restrial Aerosols and Total Solar Irradiance—Introducing
the Glory Mission,” Bulletin of the American Meteoro-
logical Society, Vol. 88, No. 5, 2007, pp. 677-691.
http://dx.doi.org/10.1175/BAMS-88-5-677
[22] L. Zhu, J. V. Martins and L. A. Remer, “Biomass Burning
Aerosol Absorption Measurements with MODIS Using
the Critical Reflectance Method,” Journal of Geophysical
Research, Vol. 116, No. D7, 2011.
http://dx.doi.org/10.1029/2010JD015187
[23] A. Sanchez, T. F. Smith and W. F. Krajewski, “A Three-
Dimensional Atmospheric Radiative Transfer Model
Based on the Discrete-Ordinates Method,” Atmospheric
Research, Vol. 33, No. 1-4, 1994, pp. 283-308.
http://dx.doi.org/10.1016/0169-8095(94)90024-8
[24] Z. Li, P. Goloub, C. Devaux, X. Gu, Y. Qiao, F. Zhao and
H. Chen, “Aerosol Polarized Phase Function and Single-
Scattering Albedo Retrieved from Ground-Based Meas-
urements,” Atmospheric Research, Vol. 71, No. 4, 2004,
pp. 233-241.
http://dx.doi.org/10.1016/j.atmosres.2004.06.001
[25] K. N. Liou and Y. Takano, “Light Scattering by Non-
spherical Particles: Remote Sensing and Climatic Impli-
cations,” Atmospheric Research, Vol. 31, No. 4, 1994, pp.
271-298.
http://dx.doi.org/10.1016/0169-8095(94)90004-3
[26] A. Kylling, A.F. Bais, M. Blumthaler, J. Shreder and C. S.
Zerefos, “UV Irradiances during the PAUR Campaign:
Comparison between Measurement and Model Simula-
tions,” Journal of Geophysical Research, Vol. 103 No.
D20, 1998, pp. 26051-26060.
[27] G. L. Schuster, O. Dubovik and B. N. Holben, “Angstrom
Exponent and Bimodal Aerosol Size Distributions,” Jour-
nal of Geophysical Research, Vol. 111, No. D7, 2006.
http://dx.doi.org/10.1029/2005JD006328
[28] M. Hess, P. Koepke and I. Schult, “Optical Properties of
Aerosols and Clouds: The Software Package OPAC,”
Bulletin of the American Meteorological Society, Vol. 79,
No. 5, 1998, pp. 831-844.
[29] K. N. Liou, “An Introduction to Atmospheric Radiation,”
2nd Edition, Academic Press, San Diego, 2002, p. 583.
[30] M. D. King and D. M. Byrne, “A Method for Inferring
Total Ozone Content from Spectral Variation of Total
Optical Depth Obtained with a Solar Radiometer,” Jour-
nal of the Atmospheric Sciences, Vol. 33, No. 11, 1976,
pp. 2242-2251.
http://dx.doi.org/10.1175/1520-0469(1976)033<2242:AM
FITO>2.0.CO;2
[31] T. F. Eck, B. N. Holben, O. Dubovic, A. Smirnov, I.
Slutsker, J. M. Lobert and V. Ramanathan, “Column-In-
tegrated Aerosol Optical Properties over the Maldives
During the Northeast Mon-Soon for 1998-2000,” Journal
of Geophysical Research, Vol. 106, No. D22, 2001, pp.
28555-28566.
[32] T. F. Eck, B. N. Holben, D. E. Ward, O. Dubovic, J. S.
Reid, A. Smirnov, M. M. Mukelabai, N. C. Hsu, N. T. O’
Neil and I. Slutsker, “Characterization of the Optical
Properties of Biomass Burning Aerosols in Zambia dur-
ing the 1997 ZIBBEE Field Campaign,” Journal of Geo-
physical Research, Vol. 106, No. D4, 2001, pp. 3425-
B. I. TIJJANI ET AL.
Open Access OJAppS
513
3448. http://dx.doi.org/10.1029/2000JD900555
[33] Y. J. Kaufman, “Aerosol Optical Thickness and Atmos-
pheric Path Radiance,” Journal of Geophysical Research,
Vol. 98, No. D2, 1993, pp. 2677-2992.
http://dx.doi.org/10.1029/92JD02427
[34] N. T. O’Neill, T. F. Eck, B. N. Holben, A. Smirnov, O.
Dubovik and A. Royer, “Bimodal Size Distribution Influ-
ences on the Variation of Angstrom Derivatives in Spec-
tral and Optical Depth Space,” Journal of Geophysical
Research, Vol. 106, No. D9, 2001, pp. 9787-9806.
http://dx.doi.org/10.1029/2000JD900245
[35] N. T. O’Neill, T. F. Eck, A. Smirnov, B. N. Holben and S.
Thulasiraman, “Spectral Discrimination of Coarse and
Fine Mode Optical Depth,” Journal of Geophysical Re-
search, Vol. 198, No. D17, 2003, p. 4559.
[36] D. G. Kaskaoutis and H. D. Kambezidis, “Investigation
into the Wavelength Dependence of the Aerosol Optical
Depth in the Athens Area,” Journal of the Royal Meteoro-
logical Society, Vol. 132, No. 620, 2006, pp. 2217-2234.
http://dx.doi.org/10.1256/qj.05.183
[37] B. Schmid, D. A. Hegg, J. Wang, D. Bates, J. Redemann,
P. B. Russell, J. M. Livingston, H. H. Jonsson, E. J. Wel-
ton, J. H. Seinfeld, R. C. Flagan, D. S. Covert, O. Dubo-
vik, A. Jefferson, “Column Closure Studies of Lower
Tropospheric Aerosol and Water Vapor During ACE-
Asia Using Airborne Sun Photometer and Airborne in
Situ and Ship-Based Lidar Measurements,” Journal of
Geophysical Research, Vol. 108 No. D23, 2003, p. 8656.
http://dx.doi.org/10.1029/2002JD003361
[38] J. A. Martinez-Lozano, M. P. Utrillas, F. Tena, Pedros, R.,
J. Canada, J. V. Bosca and J. Lorente, “Aerosol Optical
Characteristics from Summer Campaign in an Urban
Coastal Mediterranean Area,” IEEE Transactions on
Geoscience and Remote Sensing, Vol. 39, No. 7, 2001, pp.
1573-1585. http://dx.doi.org/10.1109/36.934089
[39] D. G. Kaskaoutis, H. D. Kambezidis, N. Hatzianastassiou,
P. G. Kosmopoulos and K. V. S. Badarinath, “Aerosol
Climatology: Dependence of the Angstrom Exponent on
Wavelength over Four AERONET Sites,” Atmospheric
Chemistry and Physics, Vol. 7, 2007, pp. 7347-7397.
http://dx.doi.org/10.5194/acpd-7-7347-2007
[40] D. G. Kaskaoutis, H. D. Kambezidis, , N. Hatzianastas-
siou, P. G. Kosmopoulos and K. V. S. Badarinath, “Aero-
sol Climatology: On the Discrimination of Aerosol Types
over Four AERONET Sites,” Atmospheric Chemistry and
Physics Discussion, Vol. 7, No. 3, 2007, pp. 6357-6411.
[41] J. W. Fitzgerald, “Approximation Formulas for the Equi-
librium Size of an Aerosol Particle as a Function of Its
Dry Size and Composition and Ambient Relative Humid-
ity,” Journal of Applied Meteorology, Vol. 14, No. 6,
1975, pp. 1044-1049.
http://dx.doi.org/10.1175/1520-0450(1975)014<1044:AF
FTES>2.0.CO;2
[42] I. N. Tang, “Chemical and Size Effects of Hygroscopic
Aerosols on Light Scattering Coefficients,” Journal of
Geophysical Research, Vol. 101, No. D14, 1996, pp.
19245-19250. http://dx.doi.org/10.1029/96JD03003