Correlation of aerosol
optical parameters for
OCO channels
Yu.M. Timofeyev, Ya.A. Virolainen, A.V. Polyakov
Research Institute of Physics, St. Petersburg State
University, 198504 St. Petersburg, Russia,
Yu.M.Tim@JT14934.spb.edu
1
1. Introduction
Aerosol model consists from different components which form
aerosol types by external mixing.
Database OPAC includes 10 components (in dry state) and 13
aerosol types.
Aerosol components are characterized by:
 Aerosol Size Distribution Functions (SDF) for homogenous
spherical particles ni(r, z),
 Complex refractive index (CRI) mi (, z) = ni (, z) –i ki (, z),
 Altitude profiles of concentration Ni(z),
SDF and CRI (and optical aerosol parameters) depend on ambient
conditions (humidity, wind and etc.)
In reality, especially for some clouds, we need information about
form and orientation of the particles.
Atmospheric aerosol size distributions are often described as the
sum of n log-normal distributions,
 (log D p  log D ) 2 
n
N
pi 
i
n oN ( log D p )  
exp  


2
i 1 2  1/ 2 log i
2
log
i


where Ni – is the number concentration, D pi is the mean diameter,
and i is the standard deviation of the i t h log-normal mode. In this
case 3n parameters are necessary for the description of the full
aerosol distribution.
Characteristics of model aerosol distributions are presented in
Table 1, following the suggestions of Jaenicke (1993).
In this case for description of SDF we need 9 parameters.
2
Table 1. Parameters for Aerosol Model Distributions Expressed as the Sum of Three Log-Normal
Modes
Mode I
Mode II
log 
Dp
(cm–3)
(m)
log 
N
Dp
(cm–3)
(m)
log 
N
Dp
(cm–3)
(m
Urban
9.93 x 104
0.013
0.245
1.11 x 103
0.014
0.666
3.64 x 104
0.05
0.337
Marine
133
0.008
0.657
66.6
0.266
0.210
3.1
0.58
0.396
Rural
6650
0.015
0.225
147
0.054
0.557
1990
0.084
0.266
Remote
3200
0.02
0.161
2900
0.116
0.217
0.3
1.8
0.380
129
0.007
0.645
59.7
0.250
0.153
63.5
0.52
0.425
Polar
21.7
0.138
0.245
0.186
0.75
0.300
3 x 104
8.6
0.291
Desert
726
0.002
0.247
114
0.038
0.770
0.178
21.6
0.438
Type
N
Mode III
continental
Free
troposphere
Source: Jaencke (1993)
3
Example of SDF for urban aerosol model
o
o
o
Fig.1. Typical urban aerosol number n N , surface n S , and volume nV
distributions.
4
Altitude dependence of concentration for different
aerosols
Fig.2. Representative vertical distribution of aerosol number
concentration [Jaenicke, 1993]. A range of concentrations is
shown for marine and remote continental aerosols
Different aerosol characteristics are strongly varied in space and
time. Their variability have to be taken into account using satellite
measurements.
The statistical approach is used for developing the method for the
consideration of the aerosol influence.
A description of this approach is given in our papers [Biryulina and
Rozanov, 1990; Polyakov et al., 2001, 2003; Virolainen et al., 2004;
Timofeyev et al., 2003].
5
2. Methods for obtaining the statistical
optical characteristics of aerosols
Methods for obtaining the statistical aerosol optical characteristics
can be divided at five classes:
1. The first traditional method has been applied for long-term
measurements of aerosol microphysical characteristics in USA
[Grainger et al., 1995]. It includes calculations of optical
characteristics of aerosol ensembles {  ( , z ) ,  ( , z ) ,
x (  ,  , z ) }i by Mie algorithm from measured size distribution
functions f (r ) (SDF) and given refraction index m  n  i .
2. The second approach [Gorchakov et al., 1976a–c] uses direct
measurements of realizations of aerosol optical characteristics
{  ( , z ) ,  ( , z ) , x (  ,  , z ) }i for calculating the statistical
aerosol characteristics K  (1,  2 ) , K  (1 ,  2 ) , etc.
3. The third method [Timmerink, 2001; Drdla et al., 2003] applies an
numerical model which takes into account the evolution and
transformation of aerosol and cloud characteristics for the
simulation of the ensemble of size distribution functions (SDF)
and refraction indexes and further calculations of optical and
statistical characteristics.
4. In the fourth method [Russel et al., 1983; Burulina et al., 1990;
Gobbie, 1995; Polyakov et al., 2001], average aerosol
microphysical models and variabilities are used for the simulation
of initial ensemble of aerosol physical characteristics.
5. The fifth approach – the use of optical aerosol model (e.g. OPAC
[Hess et al., 1998; Levoni et al., 1997] for simulating the
ensemble of fraction concentrations to calculate ensembles of
aerosol optical and statistical characteristics
All the methods make it possible to calculate covariance and
cross-covariance matrices describing the statistical relations
between different microphysical and optical characteristics of
aerosol and clouds and between aerosol optical characteristics and
different atmospheric parameters.
6
3. Statistical model of tropospheric
aerosol
Model OPAC (Optical Properties of Aerosols and Clouds) [Hess et al., 1998]
based on different field experiments is used for the statistical simulation of the
variability of optical characteristics of tropospheric aerosol.
This model includes optical aerosol characteristics (for 0.25–40 m) for 10
fractions: WASO (water-soluble aerosol from different sulphates, nitrates and
other organic and compounds), INSO (insoluble particles – a mixture of dust,
soil, etc.), SOOT, MINM, MIAM, MICM, MITR (mineral quart and clay
participles), SSAM, SSCM (participles of sea salt) and SUSO (stratospheric
sulphate participles consisting mainly from sulphuric acid droplets) (see,
Table 2).
Table 2. Aerosol components of the Global Aerosol Data Set and
their main microphysical parameters (OPAC Model).
Components of the Global Aerosol Data Set
No. Aerosol Component
Name
rm
[m]


[g/cm3]
1
Water-insoluble
INSO
4.71 E-1
2.51
2.0
2
Water-soluble
WASO 2.12E-2
2.24
1.8
3
Soot
SOOT
1.18E-2
2.00
1.0
4
Sea-salt (accumulation
SSAM
2.09E-1
2.03
2.2
5
mode) (coarse mode)
Sea-salt
SSCM 1.75E+0
2.03
2.2
6
Mineral (nucleus mode)
MINM
7.00E-2
1.95
2.6
7
Mineral (accumulation
MIAM
3.90E-1
2.00
2.6
8
mode) (coarse mode)
Mineral
MICM
1.90E+0
2.15
2.6
9
Mineral-transported
MITR
5.00E-1
2.20
2.6
10
H2SO4-Droplets
SUSO
6.95E-2
2.03
1.7
On the basis of these fractions 10 regional aerosol types describing
global characteristics of earth aerosol: continental (background,
mean, turbid), urban, desert, sea (background, tropical, turbid),
arctic, antarctic aerosols were constructed (OPAC model).
7
Аnalysis of optical aerosol characteristics
Studied characteristics: the aerosol extinction coefficient (AEC), the
aerosol scattering coefficient (ASC), and the parameter of
asymmetry (PA) g (the mean scattering cosines).
Input data: statistical ensembles of optical characteristics for
different aerosol types in three spectral ranges that consist of 500
realizations of number concentration (Ni) profiles for different
aerosol fractions at 25 tropospheric altitudes (0–12 km).
Calculations: the
characteristics.
complete
covariance
matrix
of
studied
Studies:
 spectral correlations of optical characteristics,
 correlation between different optical parameters,
 optimal parameterization of optical aerosol characteristics for
three wavelengths for method for determining the aerosol type
and the solution of the inverse problem.
In Table 3 some characteristics of two local ensembles of
tropospheric aerosol – continental and sea ones - are given. The
continental model includes the models of pure and polluted
continental and town aerosols, the sea model – models of pure and
contaminated sea aerosol.
8
Table 3. Characteristics of local models of tropospheric aerosol
(layer thickness h, height of homogeneous atmosphere H, aerosol
fractions and spread of surface concentration N0).
Model
Continental
h,
H,
km
km
0–2
8
Fractions (spread of surface concentration N0)
WASO (25–35752), INSO (0.0007–1.81),
SOOT (47–212689)
2–12
8
WASO (0.8–737), INSO (0.02–0.14),
SOOT (0.6–489)
0–2
Sea
1
WASO (0.5–5592), SOOT (0.9–10019),
SSAM (0.3–33), SSCM (0.00001–0.005)
2–12
8
WASO (0.8–737), INSO (0.02–0.14),
SOOT (0.6–489)
Spectral dependence of CRI for considered
measurement spectral range
1.9
1.8
SSAM
WASO
SOOT
MITR
INSO
real part of CRI
1.7
1.6
1.5
1.4
1.3
1.2
0.6
0.8
1.0
1.2
1.4
Wavelength, m
1.6
1.8
2.0
2.2
Fig.3. Real part of complex refraction index (CRI) for different aerosol
fractions (OPAC).
9
1
0.1
imaginary part of CRI
0.01
0.001
0.0001
SSAM
WASO
SOOT
MITR
INSO
1E-005
1E-006
1E-007
0.6
0.8
1.0
1.2
1.4
Wavelength, m
1.6
1.8
2.0
2.2
Fig.4. Imaginary part of complex refraction index (CRI) for different
aerosol fractions (OPAC).
1
1
0.1
0.1
0.01
0.01
Scattering, km-1
Extinction, km-1
Spectral dependence of AEC, ASC and g for considered
measurement spectral range
0.001
WASO
INSO
SOOT
SSAM
SSCM
0.0001
1E-005
1E-006
0.001
1E-005
1E-006
1E-007
1E-007
1E-008
1E-008
1E-009
1E-009
0.8
1.2
1.6
2
Wavelength, m
2.4
WASO
INSO
SOOT
SSAM
SSCM
0.0001
0.8
1.2
1.6
2
Wavelength, m
2.4
Fig.5. Spectral dependence of AEC (on the left) and ASC (on the right)
for particles of different aerosol fractions involved in continental
and sea models of tropospheric aerosol (see Table 1).
Significant differences between AEC and ASC are only for SOOT particles,
for other fractions the scattering is the main cause of radiation attenuation
(see also Fig.4). AEC and ASC in the channel 2 m is less by an order of
magnitude, three times and 30% that those in the channel 0.76 m for
WASO, SOOT and SSAM, respectively. AEC and ASC in these channels
change slightly for INSO and SSCM.
10
1
Asymmetry parameter
0.8
0.6
WASO
INSO
SOOT
SSAM
SSCM
0.4
0.2
0
0.8
1.2
1.6
Wavelength, m
2
2.4
Fig.6. Parameter of asymmetry g (AP) of the scattering indicatrix for
different aerosol fractions involved in continental and sea models
of tropospheric aerosol (see Table 1).
Indicatrices are different for different fractions. AP values for SOOT
are close to 0 (isotropic scattering, AP=0.1–0.3) especially in the
long-wave range. APs are 0.45–0.65 for WASO and the indicatrices
for INSO, SSAM и SSCM are most elongated ahead (AP=0.8–0.9).
The AP growth at 2 m in comparison with 0.76 and 1.6 m is
observed for the fraction SOOT. This peculiarity, as we will show
further, will effect AP of constructed ensembles in free atmosphere
where besides INSO there are only particles of fractions SOOT and
WASO.
11
Optical depth (AOD) of tropospheric aerosol
0.25
Model
Continental
Maritime
Aerosol optical depth
0.2
0.15
0.1
0.05
0
0.4
0.8
1.2
1.6
Wavelength, m
2
2.4
Fig.7. Mean value (with RMS variability) of aerosol optical depth of
tropospheric aerosol in different measurement channels for
different models of tropospheric aerosol.
Mean AODs are maximal for the ensemble of the continental model
and minimal for the maritime model.
In the continental model, the essential change of the mean AOD is
observed in going from the channel 0.765 m to the channel
2.016 m.
The mean AOD value at 0.765 m for the continental model is twice
as large in comparison with the maritime model. Mean AODs are
practically the same at 2.016 m for both models.
In the channel 0.765 m, the AOD RMS variability is maximal and
equal to about 60% of the mean for the continental model.
12
AOD distribution in the channel 0.765 m
100
160
80
Continental
aerosol
40
Number of cases
Number of cases
80
120
60
Maritime
aerosol
40
20
0
0
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
Aerosol optical depth
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11
Aerosol optical depth
Fig.8. AOD distribution at 0.765 m for ensembles of continental (on the
left) and maritime (on the right) models.
The most part of AOD values (from 500 realizations) falls at 0.05–
0.15 and 0.045–0.065 for continental and maritime models,
respectively.
In the ensemble of aerosol continental model, there are more dense
realizations of tropospheric aerosol.
13
4. Correlations of optical parameters
12
10
AEC 1.607 m
AEC 2.061 m
ASC 0.765 m
ASC 1.607 m
ASC 2.061 m
AP 0.765 m
AP 1.607 m
AP 2.061 m
Altitude, km
8
6
4
2
0
-0.8
-0.4
0
Correlation coefficient
0.4
0.8
Fig.9. Correlation between AEC in the channel 0.765 m and other
aerosol parameters for ensemble of continental aerosol.
12
10
AEC 1.607 m
AEC 2.061 m
ASC 0.765 m
ASC 1.607 m
ASC 2.061 m
AP 0.765 m
AP 1.607 m
AP 2.061 m
Altitude, km
8
6
4
2
0
-0.8
-0.4
0
Correlation coefficient
0.4
0.8
Fig.10. Correlation between AEC in the channel 0.765 m and other
aerosol parameters for ensemble of maritime aerosol.
14
Correlation coefficients (CC) are different for two models mainly in
the boundary layer, as in generating the ensembles for both models
in the free troposphere (above 2 km – see Table 3), we used the
same statistical data.
Comparing Fig.9 and 10, one can see that the AEC-ASC correlation
in the layer 0–2 km is higher for the narrower ensemble of maritime
model. CC between AEC at 0.765 m and AEC (ASC) in other
channels exceeds 0.90–0.95 and CC between AEC and ASC is
close to 1.
For the continental aerosol (Fig.9), in troposphere (0–2 km), CC
between AEC and ASC at 0.765 m is 0.75–0.85 depending on
altitude. Similar situation is for CC between AEC at 0.765 m and
ASC in other channels (0.65–0.75 and 0.50–0.65 in channels 1.607
and 2.061 m, respectively). This fact is explained by the influence
of the fraction of soot particles SOOT.
CC between AECs in different channels is also smaller for
continental aerosol than for maritime aerosol (about 0.95 for the
channel 1.607 m and 0.85 for the channel 2.061 m) due to the
greater spectral AEC variability in the model of continental aerosol.
Correlations between AEC and the indicatrix (AP) are practically
absent for the maritime aerosol and CC equals to  0.55 (negative)
on the average for the continental model.
In free troposphere, CCs between AEC at 0.765 m and AEC
(ASC) in channels 1.607 and 2.061 m are 0.8 and 0.6 on the
average, respectively, and little variable along altitude. CC between
AEC at 0.765 m and AP is negative and equals to about 0.8. High
CC values in free troposphere is determined by a small variability of
AP and AEC at each atmospheric level.
In constructing the models, the troposphere was classified as two
layers – the boundary layer (local ensembles) and the free
troposphere (ensembles similar in statistical characteristics for two
models). Therefore further we will consider three ensembles: the
boundary continental, the boundary maritime and the free
troposphere (see Table 3).
15
Correlation between AEC at 0.765 m and other optical
parameters
1
0.8
Correlation coefficient
0.6
Continental
Maritime
Free troposphere
0.4
0.2
AEC
ASC
AP
0
-0.2
-0.4
-0.6
-0.8
-1
0.8
1.2
1.6
Wavelength, m
2
Fig.11. Spectral dependence of CC between AEC at 0.765 m and other
optical parameters in different measurement channels for
different ensembles of tropospheric aerosol. (* – CC between
natural logarithms of AEC and ASC.)
It is seen that there are significant correlations (CC=0.85–0.99)
between AEC in the channel 0.765 m and AEC and ASD in other
channels. The exception is the ensemble of the continental model
for which AEC–ASD correlation coefficient decreases from 0.8 at
0.765 m to 0.55 at 2.061 m. Correlations between AEC and SP
are essentially smaller and practically do not depend on wavelength
(CC is close to 0 for the maritime model, CC=0.40–0.45 for the free
troposphere, CC=0.55 (in an absolute value) for the continental
aerosol.
Spectral dependence marked by asterisks shows that there is a
possibility to enhance correlations between AEC and ASD for the
continental model using the connection between logarithms of
parameters. For other models such increase of CC is not observed.
16
6. Optimal parameterization of spectral
dependence of optical aerosol
parameters
Availability of a statistical ensemble of aerosol parameters gives a
possibility to parameterize any spectral dependence by the
expansion into eigenvectors of relevant covariance matrix (into an
empirical orthogonal basis). This expansion is optimal in the sense
of obtaining the minimal parameterization errors.
Optimal parameterization of any parameter (AEC, ASC or AP)
[Oboukhov, 1959]  i :
 i    i    a p f p  i 
p 1,n
f p  i  are eigenvalues of spectral covariance
parameter, a p are relevant expansion coefficients.
Here
matrix of an aerosol
Parameterization based on Angstrom relation [Lenoble and
Pruvost, 1983]:
    0  a
Here
0
and
a
are some parameters.
17
Comparison of two parameterizations
Table 4. Errors of two parameterizations of aerosol parameters for
different ensembles of tropospheric aerosol
Type
Angstrom
Optimal
Parameter
Continental
Maritime
Free
0–2 km
0–2 km
troposphere
AEC
5.9%
3.9%
2.1%
ASC
9.9%
4.1%
1.2%
AP
5.4%
1.4%
6.5%
AEC
0.3%
0.03%
0.02%
ASC
0.3%
0.02%
0.02%
AP
1.5%
0.04%
0.07%
It is seen a significant advantage of the optimal parameterization,
especially for AEC in the continental model, when the absorption
plays the principal role in the aerosol extinction caused by soot
particles.
Errors of spectral approximation are 0.02–0.3% for AEC and ASC
and 0.04–1.5% (2% for the continental ensemble) for AP in the
case of optimal parameterization. Those are 1.2–9.9% for all
parameters and aerosol types in the case of Angstrom
parameterization.
18
7. Conclusion and recommendations
1. Global and a number of regional statistical models (continental,
maritime, free troposphere) of aerosol optical characteristics
have been constructed by numerical modelling. The first two
moments (mean and covariance matrices) of the ensembles of
optical parameters were calculated. It is shown that AEC, ASC
and AP are the most variable in the continental ensemble.
2. Correlations between different aerosol parameters in the
channels 0.765, 1.607 и 2.061 m have been studied. It is shown
that there are significant correlations between AEC and ASC in
all channels. CC between natural logarithms of these parameters
is 0.7–1.0 depending on the model, the channel and the
parameter. Correlations between AEC and AP are essentially
less (0.05–0.55) and do not depend on wavelength. CC between
values of a parameter in different channels is 0.5–1.0.
3. Errors of the approximation of AEC, ASC and AP spectral
dependence by the methods of optimal parameterization and
Angstrom have been analyzed. Errors of approximating the
aerosol parameters averaged over three channels are 0.02–1.5%
and 1.2–9.9% for optimal and Angstrom parameterizations,
respectively. Errors of optimal parameterization does not exceed
0.1% in several channels for the maritime and the free
troposphere models. The error of Angstrom parameterization for
AEC and ASC increases with wavelength and for ASC in the
channel 2.061 m ranges up to 22% for ensemble of continental
aerosol.
19
Recommendations
It is necessary:
 to proceed with the construction of statistical models of
optical characteristics of tropospheric aerosol of different
types (including the consideration of the polarization) and
numerical studies of statistical spectral and altitudinal
relations between different optical characteristics.
 to study variations of outgoing radiance in different OCO
channels caused by variations of microphysical and optical
characteristics of tropospheric aerosol. It is possible to
calculate the measurement "effective noise" caused by
variations of aerosol characteristics and to analyze different
methods for the aerosol accounting in solving the inverse
problem with respect to the column amount CO2 .
 to analyze available experimental data (or to organize
special measurements) for studying the statistical relations
(spectral,
altitudinal)
between
different
optical
characteristics of tropospheric aerosol.
20
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