In the Aerosol Robotic Network (AERONET) retrieval algorithm,
smoothness constraints on the imaginary part of the refractive index provide control of retrieved spectral dependence of aerosol absorption by preventing the inversion code from fitting the noise in optical measurements and thus avoiding unrealistic oscillations of retrievals with wavelength. The history
of implementation of the smoothness constraints in the AERONET retrieval
algorithm is discussed. It is shown that the latest version of the
smoothness constraints on the imaginary part of refractive index, termed
standard and employed by Version 3 of the retrieval algorithm, should be
modified to account for strong variability of light absorption by brown-carbon-containing aerosols in UV through mid-visible parts of the solar
spectrum. In Version 3 strong spectral constraints were imposed at high
values of the Ångström exponent (440–870 nm) since black carbon was assumed to be the primary absorber, while the constraints became increasingly relaxed as aerosol exponent deceased to allow for wavelength dependence of absorption for dust aerosols. The new version of the smoothness constraints on the imaginary part of the refractive index assigns different weights to different pairs of wavelengths, which are the same for all values of the Ångström exponent. For example, in the case of four-wavelength input, the weights assigned to short-wavelength pairs (440–675, 675–870 nm) are small so that smoothness constraints do not suppress natural spectral variability of the imaginary part of the refractive index. At longer wavelengths (870–1020 nm), however, the weight is 10 times higher to provide additional constraints on the imaginary part of refractive index retrievals of aerosols with a high Ångström exponent due to low sensitivity to aerosol absorption for
longer channels at relatively low aerosol optical depths. The effect of
applying the new version of smoothness constraints, termed relaxed, on
retrievals of single-scattering albedo is analyzed for case studies of
different aerosol types: black- and brown-carbon-containing fine mode
aerosols, mineral dust coarse mode aerosols, and urban industrial fine mode
aerosol. It is shown that for brown-carbon-containing aerosols employing the relaxed smoothness constraints resulted in significant reduction in
retrieved single-scattering albedo and spectral residual errors (compared to standard) at the short wavelengths. For example, biomass burning smoke cases showed a reduction in single-scattering albedo and spectral residual error at 380 nm of ∼ 0.033 and ∼ 17 %, respectively,
for the Rexburg site and ∼ 0.04 and ∼ 12.7 % for the Rimrock site, both AERONET sites in Idaho, USA. For a site with very
high levels of black-carbon-containing aerosols (Mongu, Zambia), the effect
of modification in the smoothness constraints was minor. For mineral dust
aerosols at small Ångström exponent values (Mezaira site, UAE), the spectral
constraint on the imaginary part of the refractive index was already relaxed in
Version 3; therefore the new relaxed constraint results in minimal change. In the case of weakly absorbing urban industrial aerosols at the GSFC site,
there are significant changes in retrieved single-scattering albedo using
relaxed assumption, especially reductions at longer wavelengths:
∼ 0.016 and ∼ 0.02 at 875 and 1020 nm, respectively, for 440 nm aerosol optical depth (AOD) ∼ 0.3. The modification of smoothness constraints on the imaginary part of the refractive index has a minor
effect on retrievals of other aerosol parameters such as the real part of the
refractive index and parameters of the aerosol size distribution. The
implementation of the relaxed smoothness constraints on the imaginary part
of the refractive index in the next version of the AERONET inversion algorithm
will produce significant impacts at some sites in short wavelength channels
(380 and 440 nm) for some biomass burning smoke cases with significant
brown carbon content and possibly in mid-visible channels (500 and 675 nm)
to near-infrared channels (870 to 1020 nm) for some urban industrial
aerosol types. However, most differences in single-scattering albedo
retrievals between those applying the new relaxed constraint and the standard
constraint will be within the uncertainty of the single-scattering albedo
retrievals, depending on the level of aerosol optical depth, Ångström exponent, brown carbon content and wavelength.
Introduction
The Aerosol Robotic Network (AERONET) (Holben et al., 1998) of globally
distributed ground-based sun–sky radiometers provides measurements of total
atmospheric column spectral aerosol optical depth (AOD; see the list of
abbreviations in Appendix A) and inversion algorithm retrievals of column-integrated aerosol particle size distribution (PSD) and complex index of
refraction (CIR). The AOD measurements have been frequently utilized for
satellite validation purposes (Sayer et al., 2018, 2019; Levy et al., 2013,
2015; Holzer-Popp et al., 2013; Lyapustin et al., 2018; Kahn et al., 2010;
Limbacher and Kahn, 2019; Ahn et al., 2014; Choi et al., 2018) plus as input
to the inversion algorithm along with directional sky radiances over a range
of scattering angles. The AOD is measured at high accuracy (Eck et al.,
1999; ∼ 0.01 in visible and near infrared and ∼ 0.02 in the UV), thereby providing a strong bound on the inversion results,
especially since the sky radiance uncertainty combined with
extraterrestrial flux uncertainty is ∼ 5 % (Sinyuk et al.,
2020). The retrieved aerosol parameters are often used in development of
satellite retrieval algorithms which must sometimes assume some aerosol
optical and physical properties (Remer et al., 2005; Lyapustin et al., 2018).
The retrievals of aerosol parameters are performed by the AERONET aerosol
inversion algorithm which was developed by Dubovik and King (2000) and
refined by Dubovik et al. (2006) with the addition of non-spherical
(spheroidal) scattering. The latest version of the algorithm employed in
AERONET Version 3 (V3) is described in detail in Sinyuk et al. (2020). The
data quality assurance procedures and cloud screening of AOD in V3 are
presented in Giles et al. (2019). The standard AERONET aerosol retrieval
product is obtained by inverting measurements taken at four standard
wavelengths: 440, 675, 875 and 1020 nm. However, the V3 aerosol retrieval
algorithm can invert extended sets of wavelengths including the UV at 380 nm
(Sinyuk et al., 2020). Absorption at 380 nm is particularly important as
this is the wavelength range in which satellite observations and algorithms are
able to retrieve atmospheric column absorption from existing (Jethva et al.,
2014) and future satellite sensors (Werdell at al., 2019). The unique
utility of measurements in UV for satellite remote sensing is related to
increased sensitivity to aerosol absorption due to absorption of molecular
scattering by aerosols (e.g., Torres et al., 1998). In addition to PSD
parameters and spectral CIR, which are directly retrieved by the aerosol
retrieval algorithm, other aerosol characteristics such as single-scattering
albedo (SSA), absorption optical depth, asymmetry parameter, lidar and
depolarization ratios are calculated from the retrieved aerosol parameters.
In general, inverted measurements have limited information content, resulting
in non-uniqueness of the solution and high sensitivity to random measurement
errors. In the worst-case scenario, an inversion fits the measurement noise
(overfitting of the data), causing non-realistic oscillation in retrieved
functions (e.g., Twomey, 1977). To prevent overfitting of the data,
additional constraints on the retrieved functions should be imposed. These
constraints usually restrict the norm of the solution or the norm of its
derivatives (e.g., Dubovik, 2004; Aster et al., 2013) and are called
smoothness constraints. The strength of the smoothness constraints should be
selected in an optimal way as to prevent non-uniqueness of solution and
overfitting of the measurements and yet not to overconstrain and suppress
the natural variability of retrieved functions. In addition, stronger
smoothness constraints should be optimally imposed at those ranges of
solution variability which are not sufficiently constrained by the
measurements. For example, for high-Ångström-exponent (AE) aerosols (fine-mode-dominated) measurement sensitivity to the imaginary part of the refractive
index (IPRI) at longer wavelengths is limited due to low AOD at these
wavelengths. The AERONET aerosol retrieval algorithm employs two types of
smoothness constraints: (1) size dependence of PSD is constrained by
restricting the norm of the third derivatives, and (2) the spectral
dependencies of the real and imaginary parts of the refractive index are
constrained by restricting that of the first derivatives (Dubovik and King,
2000).
The IPRI is one of the key retrieved aerosol parameters largely defining SSA
which plays the central role in estimation of aerosol radiative forcing and
atmospheric heating (Haywood and Boucher, 2000; Jacobson, 2001; Bond et
al., 2013; Myhre et al., 2013). The optimal selection of the IPRI smoothness
constraints and its effect on retrieved aerosol parameters is the subject of
this paper. Throughout the development of the AERONET aerosol retrieval
algorithm different implementations of the IPRI smoothness constraint were
employed. The latest V3 implementation imposes weak smoothness constraints
on the spectral dependence of the IPRI for low-AE aerosols and strong
smoothness constraints for high-AE aerosols with linear interpolation on AE
between these two cases. The first assumption works reasonably well for
coarse-mode-dominated mineral dust aerosols which exhibit high IPRI spectral
variability in UV to mid-visible parts of the solar spectrum, and the second
assumption is suitable for aerosols whose chemical composition is dominated
by black carbon (BC) exhibiting a spectrally flat imaginary index of
refraction (Bond and Bergstrom, 2006; Kirchstetter et al., 2004). However,
for high-AE aerosols containing brown carbon (BrC), the assumption of the
strong IPRI smoothness constraints is not always suitable due to possible
strong spectral variability of absorption by these aerosols at short
wavelengths (mid-visible through the UV) (e.g., Kirchstetter and Thatcher,
2012).
This paper describes the modification of V3 assumptions on the IPRI
smoothness constraints (standard, STD) to accommodate a priori information
on spectral variability of the IPRI for different aerosol types. Section 2
discusses the history of implementation of the IPRI smoothness constraints
in the AERONET aerosol retrieval algorithm and presents the new
implementation, which is termed relaxed smoothness constraints (REL). In
Sect. 3 we describe the effect of the REL smoothness constraints on SSA
retrievals by analyzing case studies for different aerosol types.
Comparisons of aerosol parameters retrieved by the AERONET aerosol retrieval
algorithm using both REL and STD assumptions on the IPRI smoothness
constraints are presented in Sect. 4. Section 5 shows examples of
comparison of both REL and STD SSA retrievals to SSA derived from in situ
measurements. The summary and conclusions are presented in Sect. 6.
Theory
The AERONET aerosol retrieval algorithm, like that of GRASP (Dubovik et al.,
2011, 2021), is based on the multi-term least-squares method
(LMS) approach, which was developed over the years by Oleg Dubovik with
co-authors (Dubovik et al., 1995; Dubovik and King, 2000; Dubovik, 2004;
Dubovik et al., 2011, 2021). The multi-term LSM concept
allows flexible incorporation of very general a priori constraints on
retrieved parameters, with emphasis on smoothness constraints in particular.
Smoothness constraints limit variability of retrieved functions such as
aerosol size distribution and spectral dependence of refractive index by
using a priori information on their derivatives. From a formal point of view
(e.g.,, Dubovik et al., 2021), the smoothness constraints are related to the
limited values of derivatives of retrieved functions, i. e. with deviations
of their mth derivatives from zero:
∂mf∂xm≈0.
For the vector of unknowns a=a1,a2,…,anT, which is a discrete representation of continuous function f, the condition (1) can be formulated as a linear system of equations
Gma+Δg∗=0∗,
where Gm is the Jacobian matrix of mth derivatives, which in
the discrete case is approximated by the matrix of mth finite differences
estimated at point a. 0∗ is the zero vector,
representing the fact that a priori estimates of the corresponding
derivatives are equal to zero. Δg∗ are the errors
reflecting uncertainty in the knowledge of the deviation of the retrieved
function f from the assumed simple functions such as constant (m= 1), straight line (m= 2), parabola (m= 3), etc. Under the assumption that the
Δg∗ values in Eq. (2) are normally distributed with
covariance matrix Cg, smoothness constraints can be easily
included in the general framework of the multi-term LMS technique to obtain the
iterative solution for vector a. For the case of a standard set
of AERONET observations (spectral AOD, spectral sky radiances) and retrieved
aerosol parameters (PSD, CIR), the solution is as follows:
∑k=12γkmKk,pTWk-1Kk,p+∑n=13γnsΩnΔap=∑k=12γkmKk,pTWk-1Δfkp+∑n=13γnsΩnap.
In Eq. (3) Δfkp=fk∗-fkp, where fk∗ represents vectors of measurements of AOD (k= 1) and sky radiances (k= 2), and
fkp represents the measurements fit at the pth iteration.
Kk,pTk= 1, 2 represents Jacobian matrices at the pth iteration of the function fk in the vicinity of ap,
and Wk denotes weighting matrices related to corresponding
covariance matrices Ck by
Wk=1εkCk,
where εk is the first diagonal element of Ck,
and γkm=ε12εk2 represents
Lagrange multipliers for different types of measurements and γns represents Lagrange multiplier for smoothness constraints for size distribution (n= 1) and real (n= 2) and imaginary parts (n= 3) of the
complex index of refraction. Jacobian matrices are the matrices of the first
derivatives of the measurements with respect to retrieved parameters, and
covariance matrices are diagonal matrices with elements equal to the
accuracy (variances) of the measurements and/or a priori estimates.
Ωn denotes smoothness matrices and is defined as
Ωn=Gm,nTWm,n-1Gm,n.
The values of Lagrange multipliers γns in Eq. (3) determine the strength of the corresponding smoothness constraints. Their selection is described in detail in Dubovik and King (2000) and Dubovik (2004), where it is
shown that theoretical values of the Lagrange multiplier can be expressed as
a function of the norm of the mth derivatives. In practice, however, it was
found both convenient and justifiable to determine the values of the
Lagrange multiplier for the smoothness constraints empirically based on
external information on the variability of the retrieved functions. For
example, if external information suggests weak variability of the refractive
index with wavelength, the value of the Lagrange multiplier can be adjusted
to force spectral dependence of the refractive index to be spectrally flat. From
other hand, if substantial spectral variability is expected, the strength of the
smoothness constraint should be relaxed.
The primary goal of smoothness constraints on the IPRI is to provide control
of retrieved spectral dependence of aerosol absorption by preventing an
excessive destabilizing effect of measurement noise on the solution and thus
avoiding unrealistic oscillations of retrievals with wavelength. Also, they
help in stabilizing retrievals of absorption of radiation for high-AE
aerosols at long wavelengths by constraining its spectral dependence based
on a priori information. The long wavelengths in these high-AE cases often
have AOD that is too low to contain sufficient information content on
particle absorption.
The AERONET aerosol retrieval algorithm employs constraints of the first
derivatives of the IPRI wavelength dependence (m= 1) in which case these constraints relate the values of the IPRI at neighboring pairs of
wavelengths. Throughout the course of algorithm development, different
approximations were used for Lagrange multipliers γ3s while assuming equal weights to all the pairs of wavelengths and thus replacing weighing matrices Wm,n with unit matrices. In version 1 (V1) of the AERONET database, it was assumed that the IPRI for all the
aerosol types is spectrally flat. This was physically justified by the flat
spectral dependence of the principal fine mode aerosol absorber, black
carbon (BC), in this wavelength range. Therefore, the strong smoothness
constraints were used with the value of γ3s equal to
10-1. In AERONET versions 2 and 3 (V2 and V3) it was
realized that such strong smoothness constraints suppress the natural
spectral variability of absorption of dust aerosols (low AE), especially for
the short wavelength visible (440 nm), but still assumed flat spectral
independence of the IPRI for fine mode aerosols. The Lagrange parameter
γ3s was linearly interpolated by AE (440–870 nm) between “pure” dust (AE = 0.001, γ3s=10-6) and “pure” fine mode aerosol (AE = 2.5, γ3s=10-1).
After incorporating the vector radiative transfer model SORD (Korkin et al.,
2017) in the V3 aerosol retrieval algorithm (Sinyuk et al., 2020), it became
possible to invert an extended set of wavelengths including in the near UV
(380 nm). In this case however, the assumption on spectral independence of
the IPRI for fine mode aerosols might not be very realistic for the high-AE
aerosols containing BrC with strong UV absorption (e.g., Mok et al., 2016).
Therefore, the V3 assumption for the IPRI smoothness constraints should be
modified by relaxing its strength at short wavelengths but keeping larger
γ3s values at longer wavelengths where measurement signal is low, thus making strength of the smoothness constraints spectrally
dependent. This can be accomplished by adjusting the elements of the weight
matrix in Eq. (5) by using smaller weights for short-wavelength pairs and
the larger ones for those of longer wavelengths.
In the new assumption of the IPRI smoothness constraints, which we term
“relaxed smoothness constraints” (REL), the value of γ3s in Eq. (3) is kept the same as for the pure dust in V2 and V3 (10-6). The diagonal elements of the weighting matrix are equal to 1 for wavelength pairs, which, for example, in the case of six-wavelength input are 380–440, 440–500, 500–675 and 675–870 nm. However, for the 870–1020 nm
pair, the diagonal element of the weighting matrix is equal to 10, thus making the
effective value of γ3s=10-5. The performance of this
assumption is tested for different aerosol types in the following sections.
Effect of relaxed smoothness constraints for the IPRI on SSA retrievals
In this section, the effect of incorporating the relaxed smoothness
constraint in the AERONET aerosol retrieval algorithm on SSA retrievals is
analyzed for different aerosol types: brown- and black-carbon-containing
aerosols, desert dust, and urban industrial aerosols.
Aerosols containing brown and black carbon
The light-absorbing aerosols that are produced from combustion (e.g., from
biomass burning and fossil fuels) are typically classified as black carbon
or brown carbon (e.g., Adler et al., 2019; Bond and Bergstrom, 2006). BC absorbs
radiation across the entire UV–near-infrared spectrum, exhibiting little to
no spectral selectivity (the IPRI is spectrally flat). BrC possess a strong
wavelength-dependent absorption that peaks in the UV spectral region and
declines though the visible part of the spectrum (e.g., Kirchstetter and
Thatcher, 2012).
SSA retrieved using V3 assumptions on the IPRI smoothness
constants (STD) and that of relaxed constraints (REL): (a) Rexburg (AOD(440) = 1.65, AE = 1.74) and (a) Rimrock (AOD(440) = 1.33, AE = 1.79) AERONET sites.
Figure 1 shows two examples of SSA retrieved from six spectral channel
measurements at 380, 440, 500, 675, 870 and 1020 nm taken at AERONET sites
where aerosols from biomass burning were present during the time of
observations: Rexburg, Idaho, USA (43∘ N, 111∘ W), on 6 August 2017 (Fig. 1a) and Rimrock, Idaho, USA (46∘ N, 116∘ W), on 23 August 2018 (Fig. 1b). The AE was high for both of these cases, AE (440–870 nm) = 1.74 for the Rexburg case
and AE = 1.79 for the Rimrock retrieval case, thereby imposing strong
constraints on spectral IPRI in the V3 or STD retrievals. It is noted that
the AOD was very high for both of these cases (Rimrock: 1.65 at 440 nm and
0.35 1020 nm; Rexburg: 1.32 at 440 nm and 0.27 at 1020 nm), thereby providing a large aerosol signal at most wavelengths and thus enabling very accurate retrievals of absorption information (Sinyuk et al., 2020). High-AOD events dominated by fine mode particles (high AE) in the northern US Rocky Mountain region in June–October are dominated by biomass burning emissions. Sky radiances at 440 to 1020 nm for these measurements
were calibrated using an integrating sphere (e.g., Holben et al., 1998)
while the vicarious method (e.g., Li et al., 2008) was used for calibration
at 380 nm since the sphere does not provide high enough radiance output in
the UV. Figure 1 displays two types of SSA retrievals: the first, depicted as
STD, was obtained by inversion using the V3 assumption on the IPRI
smoothness constraints, and the second, depicted as REL, is the result of
inversion employing the new assumption on spectral IPRI while all other
aspects remain the same. Two major features are displayed in Fig. 1: a
significant decrease in SSA retrieved using REL at the shortest wavelengths
(380 and 440 nm) and a reduction in corresponding residual error values at
these channels. The residual is the root mean square difference between the
measured sky radiances and those computed based on the retrieved aerosol
parameters. For example, the reduction in SSA in the Rexburg case is
∼ 0.033 and ∼ 0.013 at 380 and 440 nm,
respectively, while at longer wavelengths, the difference in SSA retrieved
using REL and STD assumptions is less than 0.01. The spectral dependence of
SSA retrieved using the REL assumption is qualitatively consistent with that of BrC absorption (e.g., Mok et at al., 2016). The absolute reduction
(difference between the STD and the REL residual errors) in residual values
in the Rexburg case is ∼ 17 % and ∼ 5 % at
380 and 440 nm, respectively, implying more accurate SSA retrievals obtained
using the REL assumption. The retrieved spectral dependence of SSA and residuals
in the Rimrock case exhibit similar behavior: ∼ 0.04 and
∼ 0.012 decrease in SSA at 380 and 440 nm, respectively, with
correspondent reductions in spectral residuals of ∼ 11.1 %
and ∼ 2.55 %. Figure 1 shows that in both cases the SSA
absolute differences at 675 nm are comparable to that at 440 nm, which only
can partly be explained by BrC absorption due to its decrease with
wavelength. Another possible reason for that is the larger uncertainty at
675 nm than at other wavelengths in the extraterrestrial solar spectrum as
discussed in Sinyuk et al. (2020).
SSA retrieved using V3 assumptions on the IPRI smoothness
constants (STD) and that of relaxed constraints (REL) at Mongu Inn AERONET site: (a) AOD(440) = 0.49, AE = 1.85 and (b) AOD(440) = 0.89, AE = 1.97.
Figure 2 shows SSA retrieved at the Mongu Inn AERONET site in Zambia (15∘ S, 23∘ E) for cases with two different values of AOD measured at 440 nm: 0.49
(Fig. 2a) and 0.89 (Fig. 2b). The AE is high for both of these cases (1.85
and 1.97, respectively), therefore resulting in strong constraints in the
spectral IPRI in the STD retrievals. The light absorption by aerosol at this
site in the July–October burning season (Eck et al., 2003) is dominated by BC
due to savanna burning with significant flaming phase combustion production
of BC (Ward et al., 1996). Therefore inversions using STD and REL
assumptions should result in similar retrievals, assuming BC dominates over
BrC absorption. This is indeed the case as can be seen from Fig. 2. For
the lower-AOD case, the SSA and residual values corresponding to both STD
and REL assumptions are very close with SSA absolute difference below 0.0033
and that of residual values less than 0.14 %. For the higher-AOD case, the
spectral dependencies show similar behavior except for 380 nm, where the
difference in SSA and residual values is ∼ 0.017 and 3.6 %,
respectively. This increase in aerosol absorption at 380 nm can be explained
by the presence of BrC in addition to BC in aerosol composition for this
biomass burning event. Indeed Kirchstetter et al. (2004) measured a
significant BrC absorption signature in biomass burning smoke from savanna
burning in southern Africa.
SSA averaged over AOD(440) bins for the Mongu Inn AERONET site: (a) 0.4–0.43 and (b) 1.0–1.4.
SSA averaged over AOD(440) bins for the Rimrock AERONET site: (a) 0.5–0.53 and (b) 1.0–1.4.
The above example illustrates that for biomass burning aerosols dominated by
BC, the BrC also may be present in aerosol composition, with its relative
concentration possibly increasing with AOD magnitude. To check this
assumption, statistics of retrieved SSA and spectral residuals at the Mongu
Inn site were generated by averaging them over narrow AOD bins. Figure 3
shows averaged SSA and spectral residual values for two bins in AOD: 0.4–0.43 (Fig. 3a) and 1.0–1.4 (Fig. 3b). As can be seen, for the lower-AOD bin, the average SSA retrieved with the REL assumption does not show any
indication of BrC presence and is very close to that of STD retrieval, with a
maximum difference of ∼ 0.009 at 675 nm. This difference, as
before, can be attributed in part to larger uncertainty in the solar spectrum at
this wavelength. Spectral residual errors are very close for both types of
inversion, with the difference under 1 %. Figure 3b, on the other hand,
shows a slight increase in aerosol absorption at 380 nm as retrieved by
inversion using the REL assumption, with differences of ∼ 0.006
and ∼ 1.2 % for SSA and residual values, respectively. The same type
of statistics were generated for the Rimrock site and are shown in Fig. 4.
It shows averaged SSA and spectral residual values for two AOD bins:
0.5–0.53 (Fig. 4a) and 1.0–1.4 (Fig. 4b). A higher-AOD-magnitude bin for
lower AOD for this site was selected because statistics for the 0.4–0.43 bin
was not representative due to small sample size. Figure 4 shows that biomass
burning at Rimrock shows strong BrC absorption at shorter wavelengths for
AOD magnitude higher than 0.5 while, according to Fig. 3b, for Mongu Inn
BrC absorption at 380 nm is noticeable only for AOD magnitude higher than
1 (an analysis for the 0.5–0.53 AOD bin for Mongu did not show any
increase in 380 nm absorption). The magnitude of BrC absorption and its
strength relative to BC absorption (from mid-visible to UV) varies
significantly for biomass burning aerosols potentially dependent on several
factors including fuel types and moisture content, relative strengths of the
phase of combustion (flaming versus smoldering), fire intensity, and aging
processes of the aerosols (Lewis et al., 2008; Di Lorenzo et al., 2017; Wong
et al., 2019).
Desert dust aerosols
For desert dust aerosols REL and STD retrievals of SSA are expected to be
similar due to similarity between REL and V3 (or STD) assumptions and very
weak constraints on spectral IPRI for low AE in both. Figure 5 shows SSA
and spectral residual values retrieved at the Mezaira, UAE (23∘ N, 53∘ E) AERONET site for two individual cases of AOD: 0.44 (Fig. 5a) and 1.45 (Fig. 5b). The AE(440–870) was 0.24 for the case shown in Fig. 5a and 0.20
for the case in Fig. 5b; therefore both are cases dominated by coarse mode dust
(Reid et al., 2008; Eck et al., 2008). As expected, SSA retrieved using REL
and STD assumptions is very similar, with differences below 0.002 and 0.004
for AOD 0.44 and 1.45, respectively. The difference between spectral
residuals is within half a percent. The decrease in SSA at the shorter
visible and UV wavelengths is primarily due to absorption from iron oxide
content in mineral dust (Di Biagio et al., 2019). The similarity between SSA
retrieved using REL and STD assumptions also holds for SSA averaged over AOD
bins. Figure 6 shows averaged SSA and spectral residuals for two AOD bins:
0.4–0.43 (Fig. 6a) and 1.0–1.4 (Fig. 6b). The SSA differences are below
0.0006 and 0.0015 and therefore insignificant for lower and higher AOD,
respectively, with the differences in spectral residual values within 0.5 %.
SSA retrieved using V3 assumptions on the IPRI smoothness
constants (STD) and that of relaxed constraints (REL) at the Mezaira AERONET site: (a) AOD(440) = 0.44, AE = 0.24 and (b) AOD(440) = 1.45, AE = 0.2.
SSA averaged over AOD(440) bins for the Mezaira AERONET site: (a) 0.4–0.43 and (b) 1.0–1.4.
Urban industrial aerosols
Urban industrial aerosols are defined as aerosol originating primarily from
fossil fuel combustion in populated industrial regions (Eck et al., 1999).
For this analysis the GSFC, Maryland, USA (38∘ N, 76∘ W), AERONET site located
near Washington, DC, was selected. Note that this site has relatively high
SSA when compared to other urban industrial sites (Dubovik et al., 2002;
Giles et al., 2012), due to relatively low BC content. Figure 7 shows two
cases of spectral SSA retrievals corresponding to two different values of
440 nm AOD: 0.33 (Fig. 7a) and 0.49 (Fig. 7b). The AE(440–870 nm) for the
case in Fig. 7a was 1.74 and for Fig. 7b was 1.63; therefore these high AE values
resulted in strong constraint on IPRI being applied in the V3 or STD
assumption. The AOD cases with lower magnitudes were selected for this site
due to the lower average 440 nm AOD level at GSFC (0.186) compared to the
considered AERONET sites (e.g., 0.427 for Mongu Inn and 0.36 for Mezaira).
In addition, according to Sinyuk et al. (2020), average SSA uncertainties at
440 nm estimated at GSFC for AOD (440) = 0.3 are ∼ 0.03, which
is similar to the AERONET threshold of AOD(440) = 0.4 with SSA(440)
uncertainty of 0.03 for Level 2. Figure 7 shows that employing the REL
smoothness constraint assumption for IPRI reduces the values of spectral
residuals in both AOD cases, implying that the STD constraint was restricting
spectral variability of the IPRI (SSA) for this aerosol type. The absolute
SSA differences at the four standard AERONET sky radiance measurement
channels, 440, 675, 870 and 1020 nm, for the first case are 0.0045, 0.0074,
0.0163 and 0.021, respectively, which is within average uncertainties
estimated in Sinyuk et al. (2020) for this site at AOD 0.3 using the STD
assumption: 0.028, 0.034, 0.043 and 0.048. For the higher-AOD case the SSA
differences are smaller than that for lower-AOD case and within the average
uncertainties of Sinyuk et al. (2020) (in parentheses) estimated at AOD
0.5: 0.0074 (0.019), 0.0162 (0.023), 0.0154 (0.029) and 0.0135 (0.033). The SSA
differences at 380 nm are slightly larger than those at 440 nm: 0.0052 and
0.013 for Fig. 7a and b, respectively. The SSA difference at 500 nm
is in between those at 440 and 675 nm.
SSA retrieved using V3 assumptions, depicted as STD, and that of
REL on the IPRI smoothness constants at the GSFC AERONET site: (a) AOD(440) = 0.33, AE = 1.74 and (b) AOD(440) = 0.49, AE = 1.63.
SSA averaged over AOD(440) bins for the GSFC AERONET site: (a) 0.3–0.33 and (b) 0.5–0.53.
Figure 8 shows spectral dependencies of retrieved SSA at the GSFC site
averaged over narrow AOD bins: 0.3–0.33 (Fig. 8a) and 0.5–0.53 (Fig. 8b). As in the example cases analyzed before, one can see a reduction in spectral
residuals for the REL assumption and similar spectral behavior of retrieved
SSA. Also, both Figs. 7 and 8 demonstrate similar features in spectral
behavior of SSA retrieved using the REL assumption, one of which is a
slight drop in SSA values at 500 nm. The relative magnitude of this drop
depends on the SSA value at 675 nm, which was largely suppressed by the STD
assumption (larger residual value at 675 nm) while at 500 nm both STD and
REL residuals are lower than at the neighboring 675 nm and similar to each
other. One of the possible reasons for this non-smooth spectral behavior of
retrieved SSA can be explained by spectrally non-uniform (in both magnitude
and sign) sky radiance calibration coefficients which will have a stronger
effect on retrievals for weaker smoothness constraints. Figure 9 shows
results of Fig. 7a computed with SSA retrieved by inverting sky radiances
which were vicariously calibrated using the technique of Li et al. (2008).
In this vicarious method the field of view (FOV) at 870 nm was computed from sphere radiance
calibration along with the highly accurate sun calibration plus
extraterrestrial solar irradiance. Then the FOV was subsequently utilized to
determine sky radiance calibration for all other wavelengths by assuming a
constant FOV for all wavelengths. Implemented in such a way, the vicarious
calibration approach can potentially eliminate spectral non-uniformity of
calibration as well as eliminate dependence on the solar spectrum at
wavelengths other than 870 nm. Figure 9 shows that inverting vicariously
calibrated sky radiances produced smoother spectral dependence of SSA,
eliminating the slight decrease in SSA at 500 nm. Notably, all of the SSA
plots for the GSFC site (Figs. 7, 8 and 9) show a marked difference in
spectral slope from less than 675 nm to greater than 675 nm. This is likely
a result of BrC absorption in the shorter wavelengths from the organic
carbon aerosol component present in emissions from fossil fuel combustion.
Same as Fig. 7a with the addition of SSA retrieved from vicariously
calibrated sky radiances, depicted by “REL, vic”. The abbreviation “REL, sph./vic.”
refers to SSA retrieved by inverting sky radiances calibrated using the
integrated sphere at all the channels except 380 nm, which was calibrated
using the vicarious method.
Comparison of aerosol parameters retrieved using STD and REL assumptions from four-channel inversion
The comparison of retrievals obtained using REL vs. STD assumptions on the
IPRI smoothness constraints is presented for the Rexburg, Mongu, Mezaira
and GSFC AERONET sites, and results are summarized in Tables 1 through 3.
For parameters characterizing aerosol absorption, SSA comparisons are
presented instead of IPRI due to its widespread use in climate research. In
a manner similar to that of Sinyuk et al. (2020), for SSA and the real part of the
refractive index (RPRI), this analysis is done for three bins in 440 nm AOD,
which provides comprehensive comparisons by considering different levels of
sensitivity to adjustment in the IPRI smoothness constraints. For PSD
parameters, two bins in 440 nm AOD are used due to much higher stability and
the small uncertainty of aerosol size distribution retrievals. All the
tables display mean values and standard deviations of the difference between STD and REL aerosol
retrievals.
Average values and standard deviations (in parentheses) of the
difference in SSA retrievals from inversions using STD and REL assumptions
on IPRI smoothness constraints. The difference is defined as REL minus STD.
Average values and standard deviations (in parentheses) of the
difference in the real part of refractive index (RPRI) retrievals from
inversions using STD and REL assumptions on IPRI smoothness constraints. The
difference is defined as REL minus STD.
Average values and standard deviations (in parentheses) of the
difference in volume median radius (VMR) in microns and width of particle
size distribution (STD) retrievals from inversions using STD and REL
assumptions on IPRI smoothness constraints. The difference is defined as
REL minus STD.
For Rexburg, the largest difference in SSA retrievals, shown in Table 1, is
at 440 nm, with no clear dependence on the level of AOD at 440 nm. The
average difference (over AOD levels) of -0.0167 constitutes ∼ 50 % of the SSA uncertainty at 440 nm estimated in Sinyuk et al. (2020) for biomass burning aerosols (for a different site however, Mongu). The SSA differences decreased as wavelength increased with the value of ∼ 0.01 at 675 nm and the values at 870 and 1020 nm below 0.01,
which is consistent with the spectral behavior of BrC absorption. The
differences in the retrieved real part of the refractive index are shown in
Table 2. Since assumptions on smoothness constraints for RPRI were not
modified, the observed differences are small, significantly smaller than
variability in PRRI retrievals. Table 3 shows that retrieved PSD parameters
for fine mode aerosol are practically the same for STD and REL inversions while the
differences for volume median radius (VMR) for coarse mode aerosol are 0.014
and 0.01 µm for 440 nm AOD smaller and larger than 0.2, respectively.
These differences in VMR for coarse mode are not significant considering a
rather small coarse mode optical contribution for this fine-mode-dominated
total AOD, plus the large size of these coarse mode particles (VMR typically
> 3 µm).
For Mongu, the differences in SSA are very small (Table 1) as expected due
to weak spectral dependence of the IPRI for BC-dominated aerosols, and this
is the assumption applied in the STD retrievals. SSA differences at 440 nm are
smaller than 0.0001 for the first two 440 nm AOD bins. At the same time, the
difference for 440 nm AOD greater than 0.6 is larger with the value of
∼ 0.003, which may be indicative of BrC presence for this
larger aerosol loading. Tables 2 and 3 show the mean difference in RPRI and
PSD parameters, respectively. As in the Rexburg case, the difference in RPRI
retrievals is very small: 0.01 and lower. The retrieved PSD parameters are
also in very close agreement for STD and REL retrievals for both fine and
coarse modes.
For Mezaira (UAE), the results of the REL–STD comparison are shown in Tables 1, 2 and 3. Due to similarity of REL and STD smoothness constraint
assumptions for coarse mode aerosols, all three tables show very small and
insignificant differences in the retrieved aerosol parameters. Table 1 shows
that the difference in SSA retrievals is smaller than 0.0001, except at 675 nm
where the difference is smaller than 0.002. The differences in RPRI
retrievals are below 0.005 for all the wavelengths' AOD levels. The
difference in retrieved PSD parameters is also small, with the largest
difference (0.02 µm) in coarse VMR for AOD greater than 0.2, which is significantly smaller than the standard deviation of retrievals for this
parameter for this site (0.36 µm).
Table 1 shows the differences in SSA retrievals for the GSFC AERONET site.
The main feature as is displayed in Table 1 is the increase in differences
with increasing AOD level at all wavelengths. If the increase is defined as
the difference between average SSA values corresponding to the third
(> 0.6) and second (0.4–0.6) AOD bins, the values are the
following: 0.008, 0.005, 0.007 and 0.011 for 440, 675, 870 and 1020 nm,
respectively. This increase in REL–STD differences at higher AOD can be
explained by stronger smoothing of the spectral dependence of IPRI by the
STD constraints for larger AOD. This is illustrated by the different degree
of reduction in spectral residual errors for different AOD values at 440 nm.
For example, Fig. 7 shows that reductions in spectral residuals at 380 nm
are 0.68 % and 2.07 % for AOD = 0.33 and 0.49, respectively, illustrating
stronger suppression of spectral dependence of IPRI at higher AOD. Also,
like in the case studies, the 675 comparison exhibits the largest difference,
which can be at least partially explained by the largest uncertainty in
extraterrestrial solar flux at this wavelength (Sinyuk et al., 2020) as
well as possibly by spectrally non-uniform uncertainty in sky radiance
calibration coefficients. Table 2 shows a comparison of RPRI retrievals. The
agreement between STD and REL retrievals is very good, with a mean difference
below 0.003. Table 3 also demonstrates a very good agreement in retrieved
PSD parameters for this site, similar to all other sites examined.
Comparison of SSA retrieved using STD and REL assumptions to in situ
measurements
In this section SSA retrieved from AERONET observations is compared to SSA
determined from in situ measurements collected during the DRAGON-MD
(Distributed Regional Aerosol Gridded Observational Network-Maryland)
experiment in 2011 (Holben et al., 2018). The SSA values are derived from in
situ measurements made during aircraft vertical profiles of scattering and
absorption coefficients at 550 nm. For each profile, 1 s sampled values of
scattering coefficient measurements at 450, 550 and 700 nm from the
nephelometer and absorption coefficient measurements at 470, 532 and 660 nm
from the particle soot absorption photometer were provided, both from dried
air samples. At 550 nm, an additional scattering measurement at ambient
relative humidity allowed for the calculation of an ambient SSA (rather than
dried aerosol) that is more suitable for comparison with the SSAs derived
from AERONET radiance measurements. In order to produce a column SSA value
to compare with AERONET, the 1 s SSA aircraft measurements were averaged for
the duration of the profile sampling after weighting the values according to
aerosol loading (Schafer et al., 2014). The analysis of Schafer et al. (2014) had shown that SSA retrieved by AERONET (interpolated to 550 nm) was
on average 0.011 lower than the values derived from in situ profiles. In
this section we compare SSA derived from AERONET observations using both the
STD and REL assumptions on the IPRI smoothness constraints to SSA determined
from in situ measurements. The comparison is done for several temporary
AERONET sites which were set up during the DRAGON 2011 campaign in Maryland,
USA: Aldino, Beltsville, Essex and Fair Hill. The type of aerosols
that dominated the selected sites are similar to that at GSFC and can also
be defined as urban industrial. All the comparisons are made for 440 nm AOD
larger than 0.3 due to higher sensitivity to aerosol absorption for this
aerosol type (Sinyuk et al., 2020).
Comparison of SSA retrieved by V3 aerosol inversion code
employing the STD assumption on IPRI smoothness constraints and SSA retrieved by
inversion code using the REL assumption on SSA derived from in situ measurements
at Aldino AERONET site: (a) 440 nm AOD = 0.352, (b) 440 nm AOD = 0.543 and (c) 440 nm AOD = 0.7.
Figure 10 shows comparisons of SSA retrieved at the Aldino site for three
levels of 440 nm AOD: 0.352, 0.543 and 0.7. All three cases show that the
values of SSA retrieved by the V3 inversion code employing the STD assumption on
the IPRI smoothness constraints are lower than SSA derived from in situ
measurements, which is consistent with the conclusion of Schafer et al. (2014). On the other hand, the SSA values retrieved from the inversion code employing the REL constraint assumption are closer to in situ measured SSA. For the lowest 440 nm AOD value, Fig. 10a, the differences between in
situ SSA and that retrieved using STD and REL (in parentheses) assumptions
are 0.0158 (0.0024). For intermediate, Fig. 10b, and the largest, Fig. 10c, 440 nm AOD the corresponding deviations are 0.0035 (-0.0027) and
0.011 (-0.001).
Comparison of SSA retrieved by V3 aerosol inversion code
employing the STD assumption on IPRI smoothness constraints and SSA retrieved by
inversion code using the REL assumption on SSA derived from in situ
measurements: (a) Beltsville AERONET site, 440 nm AOD = 0.322, (b) Essex AERONET site, 440 nm AOD = 0.414 and (c) Fair Hill AERONET site, 440 nm AOD = 0.795.
Figure 11 shows SSA comparisons for three AERONET sites: Beltsville (440 nm
AOD = 0.322), Essex (440 nm AOD = 0.414) and Fair Hill (440 nm
AOD = 0.795). As in the Aldino cases, the SSA values retrieved from inversions
using REL assumptions on IPRI smoothness constraints are closer to SSA values
derived from in situ measurements than those retrieved by the V3 (STD
assumption) inversion code: 0.0166 (0.004) for Beltsville, 0.032 (0.018) for
Essex and 0.009 (0.0008) for Fair Hill.
The above examples demonstrate that the bias in SSA comparison reported in
Schafer et al. (2014) may be due at least in part to the strong IPRI
smoothness constraints which restricted spectral variability of IPRI for
this urban industrial aerosol type. Therefore, it is expected that analysis
based on SSA retrievals from inversions employing the REL assumption on the
IPRI smoothness constraints will result in smaller bias. However, it must
be considered that these differences are well within the uncertainty error
bars of both the in situ measured SSA and the AERONET retrieved SSA
(regardless of the constraint type on the IPRI). Therefore the “improvement”
in agreement when applying the REL constraint on the IPRI may not have much
significance.
Summary and conclusions
A modification of the assumption on the smoothness constraints of the
spectral variation in IPRI employed by V3 of the AERONET aerosol retrieval
algorithm is presented and discussed. This modification is termed relaxed
due to the weaker strength of this new smoothness constraint. It prevents
oversmoothing of the spectral dependence of the IPRI for different aerosol
types including high-AE aerosols (fine mode dominated) containing BrC. The
modification employs spectrally dependent smoothness constraints, which are
implemented by assigning different weights to different pairs of
wavelengths. The weight 10-6 is assigned to shorter wavelengths,
while weight 10-5 is assigned to the 870–1020 nm pair. This larger
weight provides a stronger constraint for longer wavelengths where sensitivity
to aerosol absorption is limited for high-AE aerosols due to low AOD.
The effect of these REL smoothness constraints on retrievals of SSA was
analyzed for different aerosol types: BrC- and BC-containing aerosols,
mineral dust, and urban industrial aerosols. Analyses have shown that the
modification of the IPRI smoothness constraints mainly affects SSA retrieved
for BrC-containing biomass burning aerosols, resulting in reduction of both
SSA and spectral residuals at shorter wavelengths (mid-visible to the UV).
For example, for SSA retrieved for specific cases at the Rexburg and Rimrock
AERONET sites (in Idaho) for biomass burning aerosol, the reduction in SSA
and residual at 380 nm are 0.033 and ∼ 17 % and 0.04 and
∼ 11.1 %, respectively. The reduction in sky radiance
residual for these cases implies more accurate SSA retrievals with the new
REL assumption since the computed sky radiances closely match the measured
values. For mineral dust and BC-dominated aerosols the effect of modified
assumptions on IPRI smoothness constraints is very small except for high-AOD
cases for BC-dominated aerosols, which show a slight increase in absorption
at 380 nm. This can be explained by an increase in BrC in aerosol
composition for high-AOD biomass burning events dominated by BC as the
primary aerosol absorber (Mongu, Zambia). The REL assumption on the IPRI
smoothness constraints results in changes of SSA and spectral residual for
urban industrial aerosols, especially reduced SSA at the longest
wavelengths. For example, the reduction in retrieved SSA is ∼ 0.016 and ∼ 0.02 at 875 and 1020 nm, respectively, for 440 nm
AOD ∼ 0.3 at GSFC.
For urban industrial aerosols at GSFC, retrieved SSA exhibited non-smooth
spectral behavior in the vicinity of 500 nm. It was assumed that this
behavior can be explained, in part, by the spectral non-uniformity (in both
magnitude and sign) of sky radiance calibration coefficients and spectral
variation in uncertainty of the assumed extraterrestrial irradiance. To
check this assumption, SSA spectral dependence was retrieved by inverting
vicariously calibrated sky radiances. Vicarious calibration employs field of
view determined empirically by matching vicarious and sphere calibrated
radiances at the 870 nm spectral channel. Designed in such a way, it minimizes
spectral non-uniformity of calibration as well as dependence on the solar
spectrum at wavelengths other than 870 nm. Inversion of the vicariously
calibrated sky radiances produced smoother spectral dependence of SSA
without an anomaly at 500 nm.
The average differences between aerosol parameters retrieved using STD and
REL assumptions are presented and analyzed for four AERONET sites: Rexburg,
Mongu, Mezaira and GSFC. The analysis confirmed the results of the case
study analysis for SSA: the largest difference is observed for BrC-containing biomass burning aerosols (Rexburg) and urban industrial aerosols
(GSFC). The average differences for SSA retrieved at these sites are within
U27 uncertainties estimated in Sinyuk et al. (2020). For mineral dust
(Mezaira) and BC-containing aerosols (Mongu) the average SSA differences are
small due to similarity in STD and REL assumptions for dust cases and due to
similarity in BC spectral variation in IPRI to the STD assumption for the
high-BC-content cases. Comparisons of the RPRI and PSD parameters showed
very close agreements because assumptions on smoothness constraints for
these parameters were not modified.
SSA retrieved from AERONET observations using both STD and REL assumptions
were compared to SSA determined from in situ measurements collected from
aircraft profiles during the DRAGON-MD experiment. The comparisons were done
for four temporary AERONET sites set up during the experiment and showed
closer agreement between SSA retrieved using the REL assumption and in situ
SSA than between in situ SSA and SSA retrieved using the STD constraint. This
can possibly be explained by the fact that the STD assumption employed in V3
resulted in over-smoothing of the retrieved IPRI.
The implementation of the relaxed smoothness constraints on the imaginary
part of the refractive index in the next version of the AERONET inversion
algorithm will produce significant impacts at some sites, with changes up to
±0.033 and ±0.013 in short wavelength channels (380 and 440 nm) for some biomass burning smoke cases with significant BrC content and
possibly up to ±0.015 in mid-visible channels (500 and 675 nm) to
near-IR channels (870 to 1020 nm) for some urban industrial aerosol types
while still being mostly within the uncertainty of the AERONET SSA retrievals,
depending on AOD level, Ångström exponent and wavelength. For mineral dust
aerosols the impact will be insignificant, while for biomass burning aerosol
dominated by BC the changes will be relatively small. The application of
this new REL constraint on the spectral variation in the IPRI is being
planned for future retrievals in Version 4 of the AERONET database. These
retrievals will therefore have increased sensitivity to absorption by BrC in
fine-mode-dominated aerosol than is currently available in the Version 3
database. Additionally, future retrievals with the added wavelengths of 380
and 500 nm will enable more accurate and robust monitoring of BrC absorption
in fine mode aerosols and iron oxides in coarse mode dust aerosols.
List of abbreviations used in paper
AbbreviationTermAODAerosol optical depthAEÅngström exponentBrCBrown carbonBCBlack carbonCIRComplex index of refractionIPRIImaginary part of refractive indexLMSLeast-squares methodPSDParticle size distributionRPRIReal part of refractive indexRELRelaxed smoothness constraintsSTDStandard smoothness constraintsSSASingle-scattering albedoVMRVolume median radiusV1Version 1 of AERONET aerosol retrieval algorithmV2Version 2 of AERONET aerosol retrieval algorithmV3Version 3 of AERONET aerosol retrieval algorithm
Code availability
Retrieval code is available on demand from aliaksandr.sinyuk-1@nasa.gov and/or david.m.giles@nasa.gov. The version of the code used in this paper is not operational yet and will be a part of upcoming Version 4 of the AERONET aerosol retrieval algorithm, which will be released in 2024.
Data availability
Research data are available on demand from aliaksandr.sinyuk-1@nasa.gov and/or david.m.giles@nasa.gov. The data used are not yet a part of the AERONET aerosol retrieval product and will be part of upcoming Version 4 of the AERONET aerosol retrieval algorithm, which will be released in 2024.
Author contributions
The development of relaxed smoothness constraints for the
AERONET aerosol retrieval algorithm is the result of joint effort of the
members of the AERONET team (listed as ASi, BNH, TFE, DMG, IS, JSS, ASm and MS) as well as researchers from outside the project (OD). Individual contributions can be summarized as follows. ASi modified AERONET retrieval code by incorporating relaxed smoothness along with OD, who developed the theoretical basis. BNH, TFE, DMG, IS, JSS, ASm and MS contributed to discussions during AERONET team meetings.
Competing interests
At least one of the (co-)authors is a member of the editorial board of Atmospheric Measurement Techniques. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The AERONET project at NASA GSFC is supported by the Earth
Observing System Project Science Office cal–val, Radiation Sciences Program
at NASA headquarters, and various field campaigns. Resources supporting this
work were provided by the NASA High-End Computing (HEC) Program through the
NASA Center for Climate Simulation (NCCS) at the Goddard Space Flight Center.
Review statement
This paper was edited by Alexander Kokhanovsky and reviewed by three anonymous referees.
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