Comparative Calibration Method Between two Different Wavelengths With Aureole Observations at Relatively Long Wavelength

Kohei Arai & Xing Ming Liang
International Journal of Applied Science (IJAS), Volume (2) : Issue (3) : 2011 93
Comparative Calibration Method Between Two Different
Wavelengths With Aureole Observations at Relatively Long
Wavelength
Kohei Arai arai@is.saga-u.ac.jp
Information Science Department
Saga University
Saga City, 840-8502, Japan
Xing Ming Liang xingming.liang@noaa.gov
Center for Satellite Application and Research (STAR),
NOAA/NESDIS,
Camp Springs, MD 20746, U.S.A.
Abstract
A multi-stage method for calibration of sunphotometer is proposed by combining comparison
calibration method between two different wavelengths with aureole observation method for long
wavelength calibration. Its effectiveness in reducing the influences for calibration due to molecular
and aerosol’s extinction in the unstable turbidity conditions is clarified. By comparing the
calculated results with the proposed method and the existing individually calibration method, it is
found that the proposed method is superior to the existing method in terms of calibration
accuracy. Namely, Through a comparison between ILM and the proposed method using band
0.87um as reference, the largest calibration errors are 0.0014, 0.0428 by PM are lower than that
by ILM (0.011,0.0489) for sky radiances with no error and -3~+3%, -5~+5% errors. By analyzing
the observation data of 15 days with POM-1 Skyradiometer, the largest standard deviation of
calibration constants by PM is 0.02016, and is lower than that by ILM (0.03858).
Keywords: Sunphotometer, Calibration, Langley Method, Modified Langley Method, Aureole,
Solar Direct Irradiance, Solar Diffuse Irradiance.
1. INTRODUCTION
Sunphotometer have been applied widely to measure aerosol optical properties for analyzing
local and global climate, such as Aerosol Robotic Network (AERONET)
1
. There are about 500
institutions of ground based aerosol monitoring by sunphotometers or skyradiometers in the
AERONET. Thus, the maintenance of the calibration constants of sunphotometers is essential in
such works, especially for monitoring of long-term variations of atmospheric turbidity [1]-[9].
It is well known that the common Langley method (CLM) is inability to assure to obtain accurate
calibration constant for sunphotometer due to the influence by unstable atmospheric extinction
[10]-[13]. In the CLM, the calibration constant is obtained by extrapolation of the plot of the
logarithm of the sunphotometer reading against atmospheric air mass to air mass 0. Large error
of calibration constant, however, it will occur as the optical depth of atmosphere changes during
the calibration period because of the unstable atmospheric turbidity. For this reason, many
previous works which focus on reducing the influence due to the unstable atmospheric turbidity in
the instrument calibration have been studied. One of the typical representatives is Improved
Langley method proposed by T. Nakajima [13]. They introduced an analysis of volume spectrum
to firstly estimate the aerosol optical depth in order to avoid the error due to the change of aerosol
optical depth in accordance with the unsteady turbidity conditions. In consequence, it made a
greater improvement for sunphotometer calibration than the common Langley method.
1
aeronet.gsfc.nasa.gov/Operational/pictures/.../Cimel_set_up.PDF

Some factors, however, such as observation errors in circumsolar radiances, the scattering of
atmospheric molecular, the estimate errors of volume spectrum and the other assumptions of
atmospheric conditions, result in insufficiency to reduce the contribution of multiple scattering by
analysis of volume spectrum. Sometime estimation errors of aerosol optical depth are also
significant. Thus the estimation accuracy of the calibration constants also becomes small by ILM,
especially for the short wavelength. On the other hand, ratio Langley method (RLM), proposed by
B.W. Forgan (1994) [12], is the method which is depend on a known calibration for a reference
wavelength to permit calibration at the others. Using this method, it is possible to improve
calibration accuracies by selecting the long wavelength with being calibrated well by ILM as a
reference to perform calibration at the others.
In the following section, a multi-stage calibration method by combining ILM with RLM to perform
calibration for sunphotometer is proposed. Results from a numerical simulation and an analysis
for the actual data measurement by skyradiometer are followed by in order to validate the
proposed method. Then conclusions and some discussions are followed.
2. ANALYSIS OF VOLUME SPECTRUM AND IMPROVED LANGLEY
METHOD
The CLM is based on the Beer-Lambert law as follows,
τmFF −= 0lnln (1)
where F and F0 are solar downward irradiances at surface and extra-atmosphere, respectively. τ
is total optical depth of atmosphere. m is atmospheric air-mass, is approximately equal to
)cos(/1 0θ as θ0 (solar zenith angle) is less than 75 . Invariance of the aerosol optical depth in
accordance with stable atmospheric condition at different solar zenith angles is necessary to
estimate high accurate solar constant in CLM. But, it is difficult to satisfy the temporal stability of
atmosphere in usual locations, except for some special region, such as high elevation of
mountain. A sensitivity analysis for calibration in different aerosol models have been performed
by M.Tanaka (1986) [11], and there were about 2.6~10% retrieval errors of the calibration
constants by means of CLM as the aerosol optical depth varies based on a parabolic variation
corresponding changes with the extent of ±10%.
To remove the influence due to variant optical depth of aerosol in accordance with the unsteady
turbidity conditions during calibration period, T.Nakajima (1996) proposed an improved Langley
method in which the calibration are performed by simultaneous measurements combining the
direct-solar and circumsolar radiation [13]. The aerosol optical depth is estimated firstly by an
analysis of volume spectrum (AVS). In this analysis, the circumsolar radiances are replaced by a
relative intensity as equation (2).
)()(
)(
)( θθωτ
θ
θ qP
Fm
F
R +=
∆Ω
= (2)
where, R(θ) is the relative intensity of circumsolar radiance, F(θ), and normalized by direct
irradiance(F), approximate air mass (m) and the solid angle(∆ ). ω is the single scattering
albedo. )(θq indicates the multiple scattering contribution. )(θP is the total phase function of
aerosols and molecules at scattering angle is θ and given by.
ωτθτωθτωθ /))()(()( mmmaaa PPP += (3)

where aω , aτ and )(θaP are the single scattering albedo, the optical depth, and the phase
function of aerosol, respectively; and mω , mτ and )(θmP are corresponding quantities of air
molecule. Assume the aerosol particle is sphere and homogeneous, by Mie theory, )(θτω aaa P
and the aerosol optical depth can be defined as,
∫=
2
1
ln)()~,,()(
r
raaa rdrvmkrKP θθτω (4)
∫=
2
1
ln)()~,(
r
r
exta rdrvmkrKτ (5)
where ),()3/4()( 4
rnrrv π= )(rn is columnar radius distribution of aerosol. λπ /2=k ,
ξinm −=~ is refractive index, )~,( mkrKext , )~,,( mkrK θ are kernel functions and can be
calculated by Mie theory. Using an inversion scheme of solving radiative transfer equation to
correct repeatedly the multiple scattering contribution, )(θq [4], an approximate solutions of
volume spectrum, )(rv , can be estimated by circumsolar radiances. Then the aerosol optical
depth also can be estimated by equation (5). Thus, equation (1) can be rewritten by
aom mFmF τττ −=++ 0ln)(ln (6)
where oτ is ozone optical depth, and the calibration constants can be obtained by extrapolation
of the plot of the left item against amτ to amτ =0. This method is referred to Improved Langley
Method (ILM). Because most of influence due to variant optical depth of aerosol in accordance
with the turbidity atmosphere can be estimated by circumsolar radiances, the estimation
accuracies of calibration constants will be improved conspicuously comparing with the CLM, with
the plot of Fln against m .
On the other hand, the influences due to the small extent (θ<30°) of the circumsolar radiation, the
scattering of atmospheric molecule, the observation errors of circumsolar radiances, the estimate
errors of the volume spectrum and the other assumptions of atmospheric conditions, result in
insufficiency to reduce the contribution of multiple scattering in solving radiative transfer equation
by inversion scheme (T. Nakajima, 1996) [13]. Some errors will occur in estimation of the aerosol
optical depth by AVS. Thus it is hardly assured to estimate the aerosol optical depth accurately
for every wavelength of sunphotometer. Figure 1 shows the difference of the aerosol optical
depth estimated by the AVS and by reanalysis of volume spectrum from skyradiometer
measurement in several days.

FIGURE 1: The Differences of aerosol optical depth by means of AVS and reanalysis of volume
spectrum from air-mass 1.5 to 4.5. Data are observed by POM-1 of Skyradiometer2
in
11/26/2003, 12/03/2003 and 12/04/2003 at Saga, Japan
It is found that the differences of aerosol optical depth between the estimation by AVS and by
reanalysis sometime are larger than 10%. It means that the estimate accuracies of calibration
constants can become low by ILM.
3. THE PROPOSED METHOD
From Figure 1, it is also found that the differences of aerosol optical depth in long wavelength are
small than that in the shorts. This is because the influences due to the multiple scattering in the
long wavelength are smaller, and the optical depth can be estimated accurately. This also means
that the estimate accuracies of the calibration constants are higher in long wavelengths than that
in the shorts. On the other hand, Ratio Langley method, proposed by B.W. Forgan (1994) [12], is
the method which is depend on a known calibration for a reference wavelength to permit
calibration at the others by assuming the relative size distribution of aerosol to remain constant as
equation (7), so that the ratio of aerosol optical depth between the different wavelengths are
assure to be constant as equation (8).
rdrfrKtAt exta ln)(),()(),( ∫= λπλτ (7)
ψλτλτλτλτ == ),(/),(),(/),( 020121 tttt aaaa
(8)
where )(rf is the relative size distribution that is dependent only on particle radius r, and )(tA
is the multiplier necessary to produce the correct size distribution at some time t. Thus the
calibrations at the other wavelengths can be performed by using the reference wavelength as
equation (9).
)()(ln))()(()(ln 010111 λτψλλτλτλ aom mFmF −=++ (9)
where 0λ , 1λ are the reference wavelength and the calibrated wavelength, respectively. ψ is a
constant. Because )( 0λτam has been calibrated well, it is calculated accurately )(ln 10 λF by
least square regression for equation (9) between the left item and )( 0λτam . It is possible to
improve calibration accuracies by selecting the long wavelength with being calibrated well by ILM
as reference to perform calibration at the others.
Therefore, a multi-stage calibration method is proposed. In the proposed method, accurate
calibration constants in the long wavelength which are estimated by ILM are used. Also it is used
as a reference to that at the other wavelengths. Because the ILM does work well in the code of
Skyrad.pack, developed by T.Nakajima (1996) [4], this code will be used in our algorithm. The
proposed process flow is shown in Figure 2.
2
It is similar to the Aureolemeter for AERONET which is manufactured by Prede Co. Ltd.

FIGURE 2: The algorithm of multi stage calibration method.
Firstly, the code Skyrad.pack.v42 is introduced in our algorithm. It includes three processes, level
0, calibration and level 1. In the level 0, based on AVS, the aerosol optical depth and the volume
spectrum are approximately estimated by the circumsolar radiation. In the calibration, the
calibrations are performed by ILM. In the level 1, on the other hand, it is used as the calibration
constants estimated by ILM, and then it is combined with the direct and sky radiances. Thus,
more accurate solution of aerosol optical depth, aerosol volume spectrum, refractive index of
aerosol can be estimated by reanalysis of volume spectrum. Consequently, it is used the aerosol
optical depth which is estimated from the level 1, i.e. reanalysis of volume spectrum, instead of
that from the level 0. Then it is performed a calibration for the reference wavelength selected to
obtain more accurate calibration constants. Finally, based on RLM, the well-calibrated at the
reference wavelength can be used for that at the other wavelengths.
4. NUMERICAL SIMULATIONS
A numerical simulation is conducted to check a validity of the proposed method by comparing to
the ILM method. The wavelengths are selected 0.4, 0.5, 0.675, 0.87 and 1.02um in accordance
with the POM-1 of Skyradiometer manufactured by Prede Co. Ltd. The reference wavelength is
set at 0.87um. The simulated data is generated by the Skyrad.pack.v42. The aerosol size
distributions are defined two modes of log-normal distributions (bi-modal) as follows
∑=
−
−=
2
1
2
2
)
log2
)log(log
exp(
log2
)(ln
i i
i
i
i rrC
rn
σσπ
(10)
where n(lnr)dlnr is the number density of particles between radii r and r+dlnr. The values of iC is
set as 1, and iσ , ir are set as same as the aerosol type observed at Saga, Japan in 2003. The
set of parameters are shown in Table 1.
No m ode C i ri(um ) σi
1 1.0 0.37 1.95
2 1.0 3.06 2.36
TABLE 1: The parameters for log-normal distribution.

The refractive index of aerosol is set m=1.50-0.01i. Solar irradiance of extra-atmosphere is set
1.0. The variation of the optical depth of aerosol with time is given as follows (Shaw, 1976) [14].
)1( 2
0 taa αττ += (11)
where 0aτ is aerosol optical depth at noon, and are set 0.1 and 0.2. α is assumed to be 0.011.
So that the aerosol optical depth changes in the extent of 0~20% of 0aτ as the air-mass vary
from 1.5 to 4.5. We set 0,-3~3%,-5~5% random errors for the sky radiances to evaluate the
calibration accuracies by ILM and the proposed method (PM). Figure 3 (a) and (b) shows the
estimate errors of aerosol optical depth by AVS and reanalysis of volume spectrum for the
wavelengths 0.4, 0.5 and 0.87µm with no error in sky radiances.
From this Figure, it may be concluded that,
(1) Estimate accuracies of the aerosol optical depth by reanalysis of volume spectrum are almost
better than that by AVS,
(2) Estimate errors of aerosol optical depth in band 0.87µm are smaller than that in 0.4 and
0.5µm. Similarly, the cases with -3~3% and -5~5% errors in sky radiances, also can be concluded
the same points as above.
Table 2(a), (b), (c) show that the comparisons of estimate accuracies of calibration constants by
ILM and PM for the aforementioned five wavelengths. From the table, it is found that the
calibration accuracies are higher by PM, especially in short wavelength 0.4µm.
To evaluate the influence of calibration accuracies due to changing of the relative size
distribution, it is set iσ and ir ±3% and ±5% change in equation (10). The calibration results
are shown in Table 3. From the table it may say that the calibration accuracies of the proposed
method are higher than that of PM in ±3% change.
5. VALIDATION THROUGH OBSERVATIONS
It is also validated the proposed method by analysis of observation data from POM-1 of
Skyradiomater. The POM-01 Skyradiometer can measure the direct, diffuse solar irradiance as
well as aureole in solar almucantar and in the principal plane. It consists of the seven filters which
the central wavelengths are at 0.315, 0.40, 0.50, 0.675, 0.870, 0.94 and 1.02µm. The filters of the
wavelength center at 0.315µm and 0.94µm are used for estimation of O3 concentration and
precipitable water, respectively. The other filters are used for aerosol optical depth
measurements. The instrument is acquired with a 0.5 half angle field of view. The instrument is
located at Saga University, and observations were performed from September 2003 to May 2004.
Data of 15 days are selected; these days are cloud-free.
(a) (b)

FIGURE 3: The estimation errors of aerosol optical depth by the method of AVS and the method
through reanalysis of volume spectrum at the wavelength of 0.4, 0.5, and 0.87µm without any
error in sky radiance measurement.
The Figure 4 shows the calibration constants at the reference wavelength estimated by ILM in the
15 days. It is found that the accuracies are high enough with the standard deviation of only 1%.
FIGURE 4: Calibration for the reference wavelength by ILM
The calibration results of ILM and PM methods are shown in Figure 5 (a) and (b) and Table 5.
Figure 5 (a) shows calibration coefficient for the wavelength of 0.4µm and 0.5µm, while Figure 5
(b) also shows calibration coefficient for 0.675µm and 1.02µm. Table 5 indicates the standard
deviations for each band in 15 days. Consequently, it is found that the standard deviation of PM
method is smaller than that of ILM method, especially at the wavelength of 0.4µm. This also
means that the number of times of calibration required for PM is less than that for ILM to attain
the same accuracies.
0.1 0.2 0.3
W V (um ) ILM PM ILM PM ILM PM
0.4 0.0008 0.0006 0.0029 0.0009 0.013 0.0014
0.5 0.0003 0.0006 0.0015 0.0006 0.01 0.0009
0.675 0.0012 0.0005 0.0006 0.0006 0.005 0.0005
0.87 0.0002 0.0002 0.0001 0.0001 0.003 0.0004
1.02 0.0002 0.0002 0.0001 0.0001 0.002 0.0004
(a) No error in circumsolar radiances
0.1 0.2 0.3
W V(um ) ILM PM ILM PM ILM PM
0.4 0.011 0.004 0.017 0.009 0.023 0.011
0.5 0.008 0.003 0.009 0.006 0.012 0.009
0.675 0.003 0.002 0.003 0.002 0.015 0.007
0.87 0.006 0.002 0.001 0.001 0.002 0.001
1.02 0.002 0.001 0.001 0.002 0.001 0.001
(b)-3%~3% random errors in circumsolar radiances
0.1 0.2 0.3
W V(um ) ILM PM ILM PM ILM PM
0.4 0.013 0.007 0.015 0.005 0.027 0.014
0.5 0.006 0.006 0.005 0.004 0.011 0.01
0.675 0.003 0.003 0.003 0.003 0.007 0.005
0.87 0.001 0.001 0.002 0.001 0.001 0.001
1.02 0.001 0.001 0.002 0.001 0.001 0.002
(c)-5%~5% random errors in circumsolar radiances.

TABLE 2: Comparison of estimation error for calibration from ILM and the proposed method as
the optical depth are 0.1, 0.2 and 0.3.
standard deviation
W V(um ) ILM PM
0.4 0.03858 0.02016
0.5 0.02219 0.01691
0.675 0.01837 0.01295
1.02 0.01022 0.00938
TABLE 3: Comparison of the Standard deviations between ILM and PM.
(a) 0.4 and 0.5µm (b) 0.675 and 1.02µm
FIGURE 5: Calibration for 0.4µm and 0.5µm by ILM and PM.
6. CONCLUSIONS
A multi stage calibration method combining Improved Langley Method with Ratio Langley Method
is proposed in this paper. From the numerical simulation, the estimation errors of aerosol optical
depth result in calibration precision decrease by ILM. Through a comparison between ILM and
the proposed method using band 0.87µm as reference, the largest calibration errors are 0.0014,
0.0428 by PM are smaller than that by ILM (0.011,0.0489) for sky radiances without any error and
-3~+3%, -5~+5% errors. By analyzing the observation data of 15 days with POM-1 of
Skyradiometer, the largest standard deviation of calibration constants by PM is 0.02016, and is
smaller than that by ILM (0.03858). Thus it may say that the proposed calibration method is
superior to the other conventional methods.
7. ACKNOWLEDGEMENTS
The authors thank Prof, T.Nakajima and Engineer, M.Yamano of Center for Climate System
Research, The University of Tokyo for their constructive comments.
8. REFERENCES
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Comparative Calibration Method Between two Different Wavelengths With Aureole Observations at Relatively Long Wavelength

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