Recently, polarimetry has been used to enhance classical photometry to infer aerosol optical properties,
as polarized radiation contains additional information about the particles.
Therefore, we have equipped the Sun–sky automatic radiometer (SSARA)
with polarizer filters to measure linearly polarized light at 501.5
We describe an improved radiometric and polarimetric calibration method,
which allows us to simultaneously determine the linear polarizers' diattenuation and relative orientation with high accuracy
(0.002 and 0.1
During the A-LIFE (Absorbing aerosol layers in a changing climate: aging, LIFEtime and dynamics) field campaign in April 2017, SSARA collected 22 d of data. Here, we present two case studies. The first demonstrates the performance of an aerosol retrieval from SSARA observations under partially cloudy conditions. In the other case, a high aerosol load due to a Saharan dust layer was present during otherwise clear-sky conditions.
According to the Intergovernmental Panel on Climate Change (IPCC), aerosols have a significant and not entirely understood impact on the Earth's climate
Aerosols can be measured from satellites and from the ground.
While the former has the advantage of global coverage,
a spatial resolution on the order of 100
Classically, aerosol microphysical properties are retrieved from multispectral measurements.
Recently, polarimetric measurements started to be included as well.
Several studies suggest that including polarimetric information in retrievals yields additional information on the aerosol.
Predating these efforts was the POLDER instrument aboard the PARASOL satellite
Polarimetric instruments require an additional calibration.
Prior work on this has been done for polarized Cimel CE318-DP Sun photometers by
Our new methodology was applied to polarized radiance measurements from the polarized Sun–sky automatic radiometer (SSARA),
taken during the A-LIFE (Absorbing aerosol layers in a changing climate: aging, LIFEtime and dynamics) field campaign.
It took place in Cyprus during April 2017 and included ground-based components,
such as lidar and radar systems, radiometers, and in situ samplers at Paphos and Limassol.
Additionally, a research aircraft with in situ instrumentation was operated from Paphos airport.
The goal of the A-LIFE project is to investigate the effects of aerosol on the Earth's radiation budget, cloud development, and atmospheric dynamics,
with a focus on absorbing aerosols, such as black carbon and desert dust.
SSARA was previously employed in the SAMUM-1 and 2, and the SALTRACE field campaigns that had similar goals
This paper consists of two parts.
Section
SSARA is a multispectral Sun photometer that has been designed and built at the Meteorological Institute Munich
The radiometer's sensor head (Fig.
SSARA sensor head with 12 direct channels (smaller diameter tubes) and three polarized channels (larger diameter at the top, left, and right). The quadrant Sun tracker is in the center; below it is a finder for manual Sun tracking.
SSARA sensor head on the alt-azimuthal mount with straylight baffle installed.
Channels 1–12 are designed for Sun radiance measurements. They are set up as pinhole optics to avoid an image of the Sun on the detectors. At these channels, the field of view (FOV) of the center point of the detectors is 1.2
The instrument can perform measurements at a maximum time resolution of about 1.6
SSARA channel configuration from 23 January 2017 onward.
The sensor head is mounted on a two-axis alt-azimuthal mount
Sunlight scattered from the glass window and possible dirt particles on it can create straylight, especially at larger scattering angles.
To minimize this effect, a baffle has been designed and built in preparation of the A-LIFE campaign.
It consists of a 24
The scan patterns and wavelengths of SSARA are similar to those of the Cimel instruments used in AERONET, allowing for comparison. However, in contrast to Cimel, it is able to measure all its channels simultaneously, because it does not use a filter wheel. For Cimel, the filter wheel sequence takes several seconds, limiting its time resolution. Also, since it is not part of an operational network, it can be operated in any mode deemed appropriate. For instance, sky radiance scans can be performed at a higher rate or even using new patterns for testing.
Polarized radiation can be described by what is known as the “Stokes vector”
The polarimetric and radiometric calibration of the sky radiance channels were recently performed at Laboratoire d'Optique Atmosphérique (LOA) in Lille, France.
To produce linear polarized light, a combination of an Ulbricht sphere and the so-called POLBOX was used
The POLBOX acts as a linear polarizer for the unpolarized light coming from the sphere.
It consists of two glass plates that can be tilted up to 65
The output DoLP of the POLBOX can be determined with a high accuracy, as the plate angle can be set with high precision.
Here,
The refractive index of air is assumed to be 1.
The plates are fabricated from Schott SF-11-type glass.
Its data sheet provides coefficients for the Sellmeier equation (Eq.
The POLBOX has a maximum tilt angle of
Polarimetric calibration setup.
The distance between the Ulbricht sphere and the POLBOX, and between the POLBOX and the SSARA sensor head are on the order of a few centimeters
along the optical axis (shown as a dashed red line).
The glass plate angle
In the Stokes–Müller formalism, interactions with optical components or the atmosphere are described by
left multiplication of the Stokes vector of the incoming radiation
In this context, a linear polarizer can be described as a linear diattenuator,
meaning its attenuation differs for the two directions of polarization.
The Müller matrix
The light entering the instrument behind the POLBOX is taken to be polarized only in the positive
It can be seen that the polarimetric (described by
It is independent of the intensity of the incoming radiation (
For the SSARA calibration on 2 February 2017, the fit of Eq. (
What remains after this calibration is the collective rotation of all channels in the sensor head,
which also includes rotations stemming from the mount.
When only the degree of linear polarization is of interest, this is not relevant.
However, this global rotation has to be known to determine the polarization angle,
which influences how the polarized radiation is divided between the
Even unpolarized channels can have a polarization sensitivity. However, channels 3, 7, and 11 are assumed to have no polarization dependence, meaning the filters fully transmit light regardless of the polarization state. In future calibration sessions, the validity of this assumption could be investigated.
Fit of Eq. (
Calibration results for measurements on 2 February 2017. The uncertainties are determined from the fit.
Channels 3, 7, and 11 are assumed to be unpolarized, so
To determine the potential error arising from neglecting the imperfections of the filters and their orientation,
a polarized radiance all-sky panorama was simulated for 500
As mentioned before, POLBOX has an uncertainty of between 0.0015 and 0.00128 in DoLP.
Simple Gaussian error propagation can be used to determine the resulting uncertainties in the calibration.
Our calibration fits measurements to Eq. (
Relative difference in measured total radiance at 500
Same as Fig.
Relative difference in measured total radiance
Same as Fig.
SSARA should be set up perfectly perpendicular to the local tangential plane, facing exactly south. However, often, this is possible only to within a few degrees. Also, SSARA is designed to be portable, so the setup procedure has to be performed regularly. Therefore, it is useful to be able to quickly install the instrument in roughly the right orientation and determine the exact alignment by correlating the positions of the mount motors with the known Sun position for times with accurate Sun tracking.
To determine the actual orientation of the mount from several known Sun positions,
we cannot directly fit the Euler angles using conventional real
East–north–up (ENU) uses the local horizon coordinate system on the tangential plane containing the observation position.
Elevation and azimuth of the Sun ( In mount (MNT), the For the gimbaled system (GMB), the mount system is rotated around the motor axes by the elevation For the sensor head (SH), the
Sketch of the SSARA instrument and the coordinate systems used for the mount calibration; ENU (black), MNT (red), GMB (green), and SH (blue).
In an ENU spherical coordinate system, the azimuth
For direct measurements with the quadrant sensor uniformly illuminated,
the Sun and viewing vector in the ENU system are assumed to be equal (to within the accuracy of the Sun tracker).
The Sun position in the ENU system is determined with the
The optimal rotation quaternion can be found by minimizing the distance between viewing vectors
However,
For the A-LIFE data, the fitting determines a non-perpendicularity of the motors
Figure
Residual between calibrated and calculated Sun positions. The average apparent size of Sun disk is used as reference (grey).
Boundaries and initial values for the aerosol parameters used in the retrieval.
For effective variance (
Langley extrapolation is a method to enable Sun photometers to retrieve the total optical depth of the atmosphere,
without the need for a radiometric calibration of the instrument in a laboratory
HaloCam images for 17 April 2017. The convective clouds in the early morning and afternoon are visible. The persisting cirrus clouds towards the evening can be seen.
Taking measurements at varying values of the air mass factor, and assuming the optical depth to be constant over time,
the logarithm of the irradiance in Eq. (
This
SSARA is usually calibrated once a year,
either around March/April or around October/November at UFS Schneefernerhaus (2650
Total AOD at 500
Our algorithm
Fine- and coarse-mode trends of aerosol optical depth (
The 1064
However, for this study, several changes have been made compared to
Additionally, the cloud screening has been revised.
Due to the higher level of noise in the measurements, the original method classified too many measurements as cloudy.
Furthermore, SSARA also provides unpolarized radiance measurements at 440 and 780
Finally, the measurement scans performed with SSARA during the A-LIFE campaign are not taken at equidistant scattering angles.
Similar to scans performed by instruments in the AERONET framework, the angular sampling rate is higher around the Sun.
This results in this area being overrepresented and therefore overweighted in the minimization procedure.
However, most of the information provided by polarization is contained in measurements at larger scattering angles.
To account for this, all measurements are weighted by the inverse of their angular sampling rate:
The following measurements have been performed during the A-LIFE field campaign.
SSARA was installed on top of a building of the University of Cyprus in Limassol (34.674
Between 6 and 28 April, SSARA continuously performed direct Sun observations.
These have been interleaved with sky radiance scans in the almucantar and principal plane at pre-selected solar zenith angles.
Almucantar plane scans have been carried out at every 5
For testing our retrieval, data from 17 and 20 April were selected for more in depth case studies.
To evaluate the retrieval performance, the same criteria were used as in the numerical studies.
These were taken from
Since the plots showing the results are the same for both days, they will be described here first.
Figures
Same as Fig.
Same as Fig.
17 April was chosen to illustrate the retrieval behavior during cloudy phases.
Around sunrise and between roughly 11:00 and 14:15 UTC, convective clouds have been present at the measurement site.
This can also be deduced from the gap in AERONET direct Sun AOD data shown in Fig.
In the early morning (until around 04:30 UTC; Fig.
In Fig.
The retrieved effective radius of the fine mode (Fig.
The retrieved real part of the refractive index changes rapidly for fine-mode particles (Fig.
20 April was a clear-sky day.
Starting in the late morning (07:00 UTC, 10:00 LT), the AOD increased.
This can be attributed to the arrival of a Saharan dust outbreak over Cyprus from the west.
Figure
With the exception of the early morning and evening,
the AOD derived from the inversion of SSARA sky radiance measurements is overestimated by sometimes more than 0.1,
when compared with the values obtained from direct Sun observations from SSARA and AERONET (see Fig.
An increase in the coarse-mode AOD is clearly visible in Fig.
The effective radius of the fine mode (see Fig.
For the real part of the refractive index (Fig.
The retrieval of microphysical and optical properties of aerosols from multispectral sky radiance observations remains a challenge, especially in cloudy conditions. Recently, the use of polarimetric information has proven to provide additional information. We introduce a new inversion method using such measurements. However, polarimetric measurements pose additional demands on the instruments, their setup and calibration. In this paper, we also present new methods to lower the effort of calibrating such an instrument and its mount. These methods are applicable to other instruments as well.
We introduced a new method for polarimetric calibration of polarized Sun and sky radiometers.
In contrast to previous calibration methods,
it can simultaneously determine orientation and diattenuation of a polarized channel.
This reduces the experimental effort, as only measurements at a single degree of polarization are necessary.
Additionally, neither correction factors nor assumptions about the filters are required.
For the calibration of our Sun photometer SSARA, the diattenuation of the linear polarizers was determined to an accuracy of 0.002 and
their rotation to within 0.1
A novel quaternion-based correction of the mount skewness reduces the pointing error of the instrument to below 32
For evaluating our retrieval using polarimetric information, 2 d of SSARA measurements from the A-LIFE field campaign have been selected for more in-depth analysis. The SSARA instrument has been calibrated with the aforementioned methods. The retrieval has been applied on principal plane and almucantar scans separately. On both days, the results differ depending on the scan pattern used, the reason for which is not fully understood.
The first case study investigates the retrieval's behavior under partly cloudy conditions.
An increase in AOD is visible around the time of convective activity.
This effect has been shown to exist due to 3-D radiative effects close to clouds in previous numerical studies.
The second day selected features clear-sky conditions with an appearing Saharan dust layer.
This layer can be observed by an increase in coarse-mode AOD retrieved from SSARA measurements,
as well as in AERONET inversion data.
With a few exceptions, the retrieval shows the tendency to overestimate the AOD when compared to values obtained from direct Sun observations.
The error sometimes exceeds 0.1 in total AOD.
The retrieval of the effective radius works well for the fine mode.
In both cases, the value is slightly too low but agrees with AERONET to within 0.1
These remaining differences in the retrieved parameters between our method and the AERONET inversion have to be examined further. As a first step, the results from A-LIFE should be compared to measurements obtained from independent instruments, such as lidar or in situ. This should also extend to times where no AERONET results are available for comparison. Moreover, our inversion scheme should be applied to measurements from other sky radiometers, such as the Cimel CE318-DP used in AERONET. This is to rule out instrument effects. However, due to the high level of precision achieved in the various calibration steps, this is an unlikely source of error. Also, the retrieval could then be evaluated using multiple polarized wavelength measurements. Vice versa, our measurements might be analyzed using different inversion algorithms. This way, systematic errors in the retrieval method can be identified. Further numerical studies with respect to the influence of the scan pattern on the retrieval results are recommended. Additionally, it would be possible to add the total AOD obtained from direct Sun observations as a constraint to our retrieval. This approach might limit the applicability to cloudy situations when no such measurements are available or the value changes rapidly. However, for clear-sky cases, this constraint would certainly improve the retrieval results. Nonetheless, our polarimetric calibration method could easily be adapted to instruments used in AERONET.
Quaternions are an extension to complex numbers.
As complex numbers can be used to describe operations – such as rotation – in 2-D space (in polar notation),
the same is true for quaternions in 3-D space
Quaternions form a non-abelian group under multiplication defined by the Hamilton product.
Therefore, quaternions do not commute under the Hamilton product.
It can be derived using the distributive and associative laws, and the identities in Eq. (
Additionally, a dot product is defined as
It can be used to induce a norm,
It can be shown that the multiplicative inverse is
As a result, for normed quaternions (
Quaternions describing spatial rotations in three-dimensional space have to be normed.
A rotation about an axis
A regular 3-D Euclidian vector
The resulting quaternion is again pure, and the rotated vector can be reconstructed.
Also, unit quaternions can be transformed into a rotation matrix that can be applied to regular Euclidean vectors.
For a unit quaternion
All SSARA measurement data taken during the A-LIFE field campaign in
Cyprus during April 2017 are available at
HG developed the code for the retrieval and the calibration, performed the calibration, processed the measurement data, and prepared the manuscript. MW and MS designed and built the SSARA instrument, respectively. LF contributed to the polarization equipment of the instrument. CE and BM assisted the interpretation of the results. CE, MW, MS, and BM also contributed to the manuscript. CE and BM prepared the proposal for the DFG project.
The authors declare that they have no conflict of interest.
The work for this paper was funded through the German Research Foundation (DFG) project 264269520
“Neue Sichtweisen auf die Aerosol-Wolken-Strahlungs-Wechselwirkung mittels polarimetrischer und hyper-spektraler Messungen”.
We thank Tobias Kölling and Markus Garhammer for their help with the calibration of the instrument.
Carlos Toledano and his team operated and maintained SSARA during most of the A-LIFE campaign.
The authors thank Holger Baars, Birgit Heese, and the Polly
This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. 264269520).
This paper was edited by Udo Friess and reviewed by Gerard van Harten and one anonymous referee.