Polarimeter retrievals can provide detailed and accurate information on
aerosol microphysical and optical properties. The SRON aerosol algorithm is
one of the few retrieval approaches that can fully exploit this information.
The algorithm core is a two-mode retrieval in which effective radius
(

We compare the performances of multimode retrievals (varying the number of modes from 2 to 10) with those based on the original (parametric) two-mode approach. Experiments with both synthetic measurements and real measurements (PARASOL satellite level-1 data of intensity and polarization) are conducted. The synthetic data experiments show that multimode retrievals are good alternatives to the parametric two-mode approach. It is found that for multimode approaches, with five modes the retrieval results can already be good for most parameters. The real data experiments (validated with AERONET data) show that, for the aerosol optical thickness (AOT), multimode approaches achieve higher accuracy than the parametric two-mode approach. For single scattering albedo (SSA), both approaches have similar performances.

Aerosols such as dust, smoke, sulfate, and volcanic ash
affect the Earth's climate by interaction with radiation (direct effect) and
by modifying the properties of clouds (indirect effect). In order to reduce
the large uncertainties in aerosol direct and indirect effects, satellite
remote sensing is of crucial importance

Accuracy requirements on aerosol properties from

There are currently a number of aerosol retrieval algorithms available

In this study, the SRON aerosol algorithm is used, which is a full inversion
retrieval approach with the first guess generated by LUT retrieval. In the
SRON aerosol algorithm, a damped Gauss–Newton iteration method is used to
solve the nonlinear retrieval problem. Phillips–Tikhonov regularization is
used as the regularization method. In the current version of the algorithm,
it is based on a bimodal description of aerosols in fine and coarse modes, both described by a lognormal size distribution. The
parameters that describe these two modes (for each mode

Both approaches have advantages and disadvantages. The bimodal approach may
not be appropriate in situations in which aerosols contain more than two modes.
Also, the retrieval of

The aim of this paper is to compare the bimodal and multimodal approaches for the retrieval of aerosols from multi-angle polarimeter (MAP) data. For this purpose we extend the SRON algorithm with the capability to perform a multimode retrieval. We then compare the approaches for synthetic measurements and for real measurements of POLDER-3 on PARASOL.

This paper is organized as follows. Section

In this section, we first describe the
methodology of the original SRON aerosol algorithm, which is referred to
as a parametric two-mode retrieval. The inversion retrieval approach is aimed
to invert a forward model equation:

Synthetic
retrievals: aerosol optical thickness (AOT) with
the parametric two-mode retrieval
(2modeRetr

Synthetic retrievals for AOT: root-mean-square error (RMSE) and bias
for the difference
between the retrieved AOT and the true AOT.
The

In the parametric two-mode retrieval algorithm, the fine and coarse modes (denoted
by superscript “f” or “c”) are characterized by the
effective radius

To retrieve the state vector from the satellite measurements, a damped
Gauss–Newton iteration method with Phillips–Tikhonov regularization is
employed

Based on the linear approximation (Eq.

Synthetic retrievals for the AOT (at 550 nm) of all the fine modes
(

Synthetic retrievals for the AOT (at 550 nm) of all the coarse
modes
(

The regularization parameter

We now introduce the multimode SRON aerosol
retrieval approach. In principle, the idea of the multimode approach is that
instead of fitting the size distribution parameters (

Multimode retrieval definition.

The performance of the multimode approach is expected to be better and better as the
mode number increases. In this study, we take the 10-mode retrieval as the
maximum mode number retrieval. All the multimode retrieval cases are defined
as in Table

Abbreviations for different retrieval cases.

Synthetic retrievals: single scattering albedo (SSA) with the
parametric two-mode retrieval
(2modeRetr

Synthetic retrievals for SSA: root-mean-square error (RMSE)
and bias for the difference
between the retrieved SSA and the true SSA.
Panels

For multimode retrievals, the state vector

State vector for parametric two-mode retrieval and multimode retrieval.

In addition to the aerosol-related parameters,

Synthetic retrievals for the real part of refractive index
(at 550 nm) of the fine modes (

Synthetic retrievals for the real part of refractive index
(at 550 nm) of the coarse modes (

Prior values and weighting factors for the state vector in the parametric two-mode retrieval
and the multimode retrieval.
The prior value and weighting factor of aerosol loading

The inversion procedure of multimode retrievals is the same as described by
Eqs. (

In the SRON aerosol algorithm, the first guess of

Parameters to create a 10-mode lookup table.

The precalculated LUT is used as input for an approximate forward model in
the LUT retrieval. Here, the RT multiple scattering
calculations, performed separately for the different modes, are combined
using the method of

The satellite data used in this study for aerosol
retrievals are from the Polarization and Directionality of Earth
Reflectances-3 (POLDER-3) instrument

Each PARASOL image including 242

In the SRON aerosol algorithm, we do not directly use

Synthetic retrievals for the imaginary part of refractive index
(at 550 nm) of the fine modes (

Synthetic retrievals for the imaginary part of refractive index
(at 550 nm) of the coarse modes (

It should also be noted that higher-accuracy aerosol retrievals are to be
expected for all parameters from instruments that have higher polarimetric
accuracy, more scattering angles, and/or more spectral bands (e.g.,

During retrievals, some atmospheric and meteorological inputs are needed to
be interpolated to each pixel (where there is a PARASOL measurement) at a
specified time and a geographical location. The required atmospheric
parameters and inputs are humidity, temperature, pressure, and height. In this study,
we obtain this information from National Centers for Environmental
Prediction (NCEP) reanalysis data

In this study we focus on aerosol retrievals over
land. We validate the retrieved AOT with AERONET
(AErosol RObotic NETwork) level 2.0 data (quality assured) of AOT

Synthetic retrievals for the central height (

In a retrieval, it is a common approach to apply
the goodness of fit (

We consider retrievals with

To evaluate the retrieved aerosol properties, two measures are used, which
are the RMSE and the bias. The two measures are both
with respect to the differences between the retrieved values and the
reference values (AERONET for real measurements and the truth for synthetic
measurements). Here the difference

Synthetic retrievals: pass rates when

For each aerosol property, the RMSE counts the overall retrieval errors for
all pixels with

To investigate the capability of multimode retrievals of aerosol
microphysical and optical properties, we first perform synthetic data
experiments. We can assess the capability of different retrieval setups by
comparing the result of the retrieval to the truth that was used to
create the synthetic measurement. The synthetic measurements are computed for
the PARASOL wavelengths and 14 viewing angles, which is representative for
PARASOL (Sect.

The synthetic measurements are created pixel by pixel with two steps.
(1) We generate aerosol modes based on assumed true aerosol properties of the
effective radius

For synthetic data experiments, we only consider noise-free retrievals; i.e., no noise is added to the generated synthetic measurements. In this way we focus the experiment on errors related to inconsistencies between the synthetic measurement and retrieval (i.e., different modes), and the capability of the retrieval algorithm itself (for consistent retrievals).

The synthetic retrievals for AOT are first evaluated. The abbreviations for
different retrieval cases are summarized in Table

Real data retrievals of AOT among 2modeRetr

Figure

We first look at the performance of the consistent 10-mode synthetic
retrieval, which is shown in Fig.

In addition to consistent retrievals, it is interesting to test the performances of
inconsistent retrievals of AOT. This is because in reality,
it is unknown
how many modes the true atmosphere contains. For this purpose,
inconsistent retrievals are also shown:
parametric two-mode retrieval on 10-mode synthetic measurements (2modeRetr

Real data retrievals for AOT: root-mean-square error (RMSE) and bias for the difference between PARASOL retrievals and AERONET data.

Next, we check the performances of other multimode
(i.e., two-,three-,

It has been investigated that the multimode retrievals are capable of retrieving AOT
(the total AOT over all modes) for both consistent and inconsistent cases.
Since each retrieval case and each measurement case include two types of modes (i.e.,
the fine and coarse types), it is interesting to test multimode retrievals on
the AOT over all fine modes (

Figure

Real data retrievals of SSA among 2modeRetr

The total AOT of the coarse modes (

We also tested multimode retrievals of SSA.
Figure

Real data retrievals for SSA: root-mean-square error (RMSE) and bias for the difference between PARASOL retrievals and AERONET data.

By comparing SSA for consistent retrieval cases
(Fig.

Figure

As described in Sect.

For the consistent retrievals (2modeRetr

For inconsistent retrieval cases, we first check the performances on the 10-mode
measurements, i.e.,
the right panel of Figs.

Next, we test the retrievals of the imaginary part of the refractive index.
The fine-mode and coarse-mode cases
(i.e.,

For consistent retrievals,

For inconsistent retrieval cases,
the performances on the 10-mode synthetic
measurements (see panels c, f, and h of Figs.

The retrievals of the central height

For the inconsistent retrievals on the two-mode synthetic measurements,
4-, 5-, 6-, 7-, 9-, and 10-mode retrievals
(RMSE

Based on the results above, we conclude that
the multimode retrievals with

The pass rate

The synthetic experiments above have shown that multimode retrievals
with

AERONET stations for validation of PARASOL retrievals.

To validate PARASOL (satellite) retrievals, AERONET (ground-based) AOT and SSA data
are used, as introduced in
Sect.

In this section, the performances of multimode retrievals for AOT are
compared to that of the parametric two-mode retrieval.
Figure

We first focus on the performances at 675 nm, i.e.,
Fig.

For real data retrievals, we set

In addition to these three retrieval cases, we also perform multimode
retrievals with different numbers of modes. The RMSE and
the bias for all the retrieval cases (2–10 modes) are shown in Fig.

Based on the results above, we can conclude that multimode retrievals generally work better for retrieving AOT than the parametric two-mode retrieval. However, multimode (except for 10-mode) retrievals have larger absolute bias than the parametric two-mode retrieval.

Section

We compare the three sub-figures in each row of Fig.

Second, we check at 440 and 875 nm whether the conclusions at 675 nm hold.
For this purpose, we look at
the first and the third
columns of Fig.

Next we validate PARASOL retrievals of SSA
with the AERONET-based SSA (described in Sect.

Similarly to what was shown for AOT (Fig.

We first check the tendency of the SSA accuracy for different wavelengths. By comparing
RMSE in each row of
Fig.

Comparing RMSE in each column of Fig.

For the PARASOL retrievals in this paper we did not retrieve the aerosol layer height
but used a fixed value of 1 km. This resulted in better AOT retrievals.
The reason for poor performance of aerosol height retrieval from PARASOL
is probably the absence of near-UV polarization measurements
in combination with the relatively poor polarimetric accuracy

In this study we compared aerosol retrievals from Multi-Angle Polarimeter (MAP) data for different definitions of the retrieval state vector: (1) a two-mode definition in which the state vector includes aerosol properties for fine–coarse modes and land or ocean surface properties; (2) a multimode definition in which the state vector excludes the effective radius and the effective variance and only retrieves the aerosol column of each mode. For the purpose of this study we extended the SRON aerosol algorithm – which was based on a parametric two-mode approach – to include capability of a multimode retrieval. To evaluate the retrieval capability for different state vector definitions, the performances between multimode approaches and the parametric two-mode retrieval approach were compared on both synthetic measurements and real (PARASOL) measurements.

In synthetic experiments, the consistent retrievals (when the number of modes for retrievals
equals the number of modes for creating synthetic measurements) show both
the multimode and parametric two-mode approaches
can reach high accuracy for most of the parameters, e.g.,
the AOT, the SSA, the
refractive index, and the aerosol height. For inconsistent retrievals
on 10-mode synthetic measurements,
the multimode retrievals with

It should be noted that the geometry used for the synthetic study in this paper is quite favorable
as it assumes measurements in the principal plane. We also performed the same synthetic
study for a much less favorable geometry (SZA

After synthetic experiments, real (PARASOL) data experiments were performed. Multimode retrievals of AOT were shown to compare better to AERONET than the parametric two-mode retrieval (e.g., RMSE 0.1230 over 0.1624). Here, we found that the agreement with AERONET improves with an increasing number of modes, with the 10-mode retrieval showing the best agreement with AERONET for AOT. For real data retrievals of SSA, both multimode and parametric two-mode retrievals have similar performances.

When comparing retrievals among different algorithms, it is important to
realize that the performance of a given algorithm depends on a number of factors,
the definition of the aerosol state vector being one of them. Other factors are the
inversion approach (cost function, regularization strength, multiple versus single pixel),
the accuracy of the forward model, and the surface reflection model.
It is important to study the abovementioned aspects with an individual algorithm.
However, now that the SRON algorithm has been extended to include an arbitrary number
of fixed modes, it has become easier to compare to other algorithms using a similar
state vector definition

The multimode approach provides an opportunity to make aerosol retrievals more computationally efficient. This is due to the fact that the effective radius and the effective variance are not retrieved in the multimode retrievals, thus the Mie–T matrix calculation for each mode can be fixed and precomputed as a function of refractive index. Then, there is no need to integrate over size distribution during the retrieval. Therefore, the most time-consuming part (as it is called many times) of the retrieval can be significantly accelerated.

The PARASOL level-1 data can be downloaded from the
website

GF and OH designed the experiments, analyzed the results, and finalized the paper.

The authors declare that they have no conflict of interest.

This work is funded by a NWO–NSO project ACEPOL: Aerosol Characterization
from Polarimeter and Lidar under project number ALW-GO/16-09. We thank
PARASOL team and AERONET team for maintaining the data. NCEP reanalysis data
were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their website
at