Visible-band and near infrared polarization and radiance images measured with a ground-based full-sky polarimeter are compared against a successive orders of scattering (SOS) radiative transfer model for 2009 summer cloud-free days in Bozeman, Montana, USA. The polarimeter measures radiance and polarization in 10-nm bands centered at 450 nm, 490 nm, 530 nm, 630 nm, and 700 nm. AERONET products are used to represent aerosols in the SOS model, while MISR satellite BRF products are used for the surface reflectance. While model results generally agree well with observation, the simulated degree of polarization is typically higher than observed data. Potential sources of this difference may include cloud contamination and/or underestimation of the AERONET-retrieved aerosol real refractive index. Problems with the retrieved parameters are not unexpected given the low aerosol optical depth range (0.025 to 0.17 at 500 nm) during the study and the corresponding difficulties that these conditions pose to the AERONET inversion algorithm.
© 2011 OSA
Over the last decade, important progress has been made toward a better understanding of the radiative effects of aerosols on climate . To develop a more accurate aerosol climatology, several surface-based  and satellite-based optical remote sensing platforms (e.g.  and ) have been deployed. Despite these advances, it is increasingly apparent that more highly constrained aerosol retrievals require the addition of polarization information to the current radiance-only methods [5–8]. The performance improvement gained by including polarization in retrievals owes to its higher sensitivity to select aerosol properties . This sensitivity also enables sky polarization measurements to be used to independently verify the accuracy of retrieved aerosol parameters from radiance-only methods.
In the past few years, we have developed a full-sky polarimetric imager [9–12]. In this study, we compare measurements of full-sky polarization against a polarized (vector) successive order of scattering (SOS) radiative transfer model  which uses aerosol products from the Aerosol Robotic Network (AERONET) . Since AERONET does not currently measure polarization (at most stations) and consequently does not use polarization in its aerosol retrievals, the accuracy of AERONET aerosol parameters can be indirectly assessed by comparing sky polarization observations with results from radiative transfer simulations which employ AERONET products. If the retrieved aerosol parameters from AERONET accurately represent the aerosols, the polarization simulated using these parameters is expected to agree with the observed polarization. In this paper, we discuss comparisons between a radiative transfer model which uses AERONET aerosol products and observations from a full-sky polarimeter.
1.1 Visible and NIR full-sky polarization and radiance measurements
The observation data reported here is generated by a visible, near-infrared (VNIR) imaging polarimeter that was developed for studying both sky polarization and ground-based object polarization signatures [9–12]. The polarimeter is capable of switching between two fields of view—a wide-angle fisheye for imaging the full sky (used exclusively here) and a narrow-angle telephoto for imaging smaller objects. At the time of study, the instrument operated in five 10-nm bands centered at 450 nm, 490 nm, 530 nm, 630 nm, and 700 nm. Two liquid crystal variable retarders (LCVRs) are used to electronically vary the retardance seen by incoming light so that a full Stokes image is measured in less than a few tenths of a second. (Intensity images from the camera are inverted by a calibration matrix to form the 4-element Stokes images.) Quick acquisition allows reliable measurements in partly cloudy skies without polarization artifacts that would arise if the clouds were to move between frames. This imager obtains polarized sky measurements with uncertainty less than (usually much less than) ± 3% in the degree of linear polarization (DoLP).
All observations here are for seven cloud-free days in late August and September 2009 in Bozeman, Montana, USA.
The Aerosol Robotic Network (AERONET) of solar radiometers measures direct solar irradiance and sky radiance across the globe . These measurements are used to calculate aerosol optical depth from direct solar irradiance measurements and to derive aerosol properties, such as size distribution, refractive index, and single scatter albedo, from a sky radiance inversion scheme . We used aerosol products provided from our AERONET instrument (which is co-located with the polarimeter) to represent aerosols in the radiative transfer model.
1.3 Successive orders of scattering (SOS) radiative transfer model
The successive orders of scattering (SOS) radiative transfer model  used in this study has been used extensively by previous investigators (e.g [15–17].) and has been compared successfully to other models . The derivative of the model that we acquired from AERONET had been slightly modified for their purposes. We further modified the model to allow direct incorporation of MISR land surface BRF products (see section 2.3).
2. Setting up the comparison
Figure 1 shows the methods used to make the comparisons discussed here: model vs. polarimeter polarization, model vs. polarimeter radiance, and AERONET vs. polarimeter radiance. The validity of the model results used in the comparisons depends heavily on the accuracy of the model parameters. The parameters that most influence the modeled sky radiance and polarization are the aerosol and molecular optical depths, the aerosol and molecular single scatter albedos, the aerosol scattering phase matrix, and the surface reflectance parameters. The methods for generating and including these variables into the SOS model are discussed in the following sections.
2.1 Aerosol scattering and absorption
AERONET products provided all aerosol properties included in the SOS radiative transfer model. Since polarimeter observation wavelengths and measurement times did not always correspond directly to associated AERONET values, AERONET parameters were linearly interpolated in wavelength and time to match the polarimeter. This interpolation was applied to aerosol optical depths, size distributions, and complex refractive indices. (The model used the “direct sun” aerosol optical depth measurements, as opposed to the retrieval-derived aerosol optical depth.) Similarly, phase functions and single-scatter albedos (SSA) provided by AERONET were not always available at the polarimeter wavelengths. Furthermore, the full aerosol scattering phase matrix–as opposed to the phase function provided by AERONET–was needed for the polarized radiative transfer model. At each polarimeter wavelength, a Mie code and T-matrix kernel lookup table provided by AERONET  were used to generate these parameters directly from the interpolated size distribution, sphericity, and complex refractive index. For AERONET size distributions below 100% sphericity, the parameters were handled in a consistent manner to AERONET. That is, the parameters were calculated for a mixture of spherical particles and spheroid particles with a fixed shape (aspect ratio) distribution–the same spheroid shape distribution used in the AERONET operational algorithm [16,19].
The aerosols were assumed to have a vertical extinction distribution described by a Gaussian centered on a 2 km height and were otherwise assumed to be homogenous throughout the column. (Physically realizable modifications to this vertical distribution did not appreciably affect the model results.)
The aerosols parameters varied significantly over the seven days studied. Figure 2 shows a representative set of retrieval aerosol parameters for each day. Roughly half of the retrieved AERONET sphericity parameters (not shown) were over 90% with the remainder being distributed roughly evenly from 0% to 90%.
2.2 Molecular scattering and absorption
While AERONET wavelengths were selected to minimize molecular absorption, the polarimeter bands were originally chosen to uniformly sample the visible/NIR spectrum without regard to molecular absorption features. The polarimeter 630 and 700 nm bands observe portions of the atmospheric spectrum with significant oxygen and water vapor absorption features, respectively. The presence of these features necessitated an accurate representation of the molecular absorption in the models.
To simulate the molecular absorption, aerosol- and cloud-free MODTRAN  transmission simulations were executed using a MODTRAN mid-latitude summer standard atmosphere. These models included the MODTRAN default atmospheric constituents (nitrogen, oxygen, ozone, nitrogen dioxide, etc.) as well as ozone and precipital water vapor products supplied by AERONET. Using the resulting MODTRAN spectral transmission, the effective total molecular optical depth of each polarimeter band was calculated from a spectral average of the MODTRAN transmittance weighted by the polarimeter band transmission. Then, the effective molecular single scatter albedo (SSA) was calculated as a ratio of the Rayleigh (molecular scattering) optical depth and the effective total molecular optical depth. While this effective molecular absorption method may not be physically exact, no appreciable differences were seen in the model results between this effective molecular absorption method, and the physically exact method which first executed the SOS model across all spectral features and then band-averaged the resulting polarized radiances. Using the former method reduced the computation time by a large factor. We found that the molecular optical depths and SSAs generated by MODTRAN for the 450 and 490 nm polarimeter bands agreed well with the AERONET-provided parameters for those bands. The SOS molecular vertical extinction distribution was set to be an exponential with an 8 km scale height in the model.
2.3 Surface reflection
Multiple scattering of surface-reflected light from aerosols and molecules greatly reduces the DoLP (while increasing the radiance) observed in ground-based sky measurements . Therefore, accurate surface reflectance parameters are needed for valid simulations. To fulfill this need, we modified the SOS code to directly incorporate BRF model parameters from the MISR satellite land surface product . MISR provides BRF parameters for a modified version of the RPV (Rahman-Pinty-Verstraete) model . (The SOS code as provided to us by AERONET implemented the standard RPV model.)
The SOS model simulates a homogenous surface. Since an individual pixel in a MISR image is not expected to properly represent an entire area, we calculated an effective BRF model for the 50 km radius area surrounding Bozeman as follows. Using the MISR BRF model parameters, the BRF values for every possible source and view angle geometry at every pixel were calculated. Then, the BRF values were averaged across all pixels according to geometry. The averaged BRF data were then fit to an effective MRPV model. The effective model was calculated for all bands in each MISR product available for the Bozeman 2009 summer. Finally, the effective MRPV model parameters were linearly interpolated to the polarimeter both spectrally and temporally before inclusion in the SOS model. (This method was also repeated for an 8 km radius area, but the SOS simulation results were not significantly different from the 50 km case.)
The SOS model allowed specification of the polarized surface using the Nadal and Breon model parameters . Since the area surrounding Bozeman is largely forested, we tried the “high NDVI forest” parameters specified in the table on pg. 1715 of , but the model results were not significantly different from the case where a completely unpolarized surface was defined.
3. Comparison results and discussion
3.1 Full sky time lapse comparisons
For each polarimeter observation, sky radiance and polarization values were simulated by the SOS model for a sparse grid of zenith and azimuth angles that covered the entire sky. Using two-dimensional interpolation, values for the remaining sky were generated. For comparison purposes, these simulated data were projected identically to the polarimeter fisheye projection. An example of both the observed data and the projected simulation data is shown in Fig. 3 . As the animation in Fig. 3 (Media 1) shows, the polarimeter and the model typically agree well, although some biases do exist.
3.2 Maximum degree of polarization comparisons
The maximum degree of linear polarization (DoLP) and its associated minimum sky radiance were selected as the parameters of interest for the comparison. (The sky region with minimum radiance is near the region with the maximum DoLP.) We have found that differences between the model DoLP and the observation DoLP across the entire sky are typically well correlated with maximum DoLP differences. If the DoLP maxima agree, the DoLPs in the remaining sky regions also generally agree. Figure 4 shows comparisons of the observations and the models for these two parameters. Data shown are for times when the polarimeter observations and the AERONET retrievals were within 10 minutes of each other.
Figure 4 shows that the model maximum DoLP is generally higher than the measured DoLP for these data. For the shorter wavelengths, this difference is typically not greater than the data variability. Also, the modeled minimum sky radiance is typically lower than observed (Fig. 5 ). Some error in the minimum sky radiance is expected since comparisons of the polarimeter and CIMEL radiances exhibit similar differences (see Appendix 1). The differences are at least partially attributable to systematic radiance errors in the calibration standards used for each individual instrument. In the case of CIMEL calibration errors, these errors would affect the retrieved aerosol parameters (and therefore the sky models) due to the aerosol model parameters being derived from the source CIMEL radiances. Therefore, radiance differences between the polarimeter and the model would be expected without preference to the source of the error. That is, radiance differences would exist whether the CIMEL or the polarimeter is the major cause of the radiance error. While radiance errors may be blamed, at least in part, on systematic errors in the instrument calibrations, polarization differences of the magnitude seen here are much higher than previous polarimeter error characterizations . A more critical analysis of potential error sources follows.
3.3 Potential sources of comparison differences
For all wavelengths, the modeled DoLP tends to be higher than observation while the radiance tends to be lower. One potential explanation for this behavior is thin cloud contamination. In our experience, thin clouds will reduce the DoLP significantly. This effect is most pronounced in the maximum DoLP sky regions and at longer wavelengths. Thin clouds also increase the sky radiance. This may explain the higher observed radiances and lower observed DoLPs. Since we would not expect cloud contaminations to be present in all observations (and AERONET quality control seeks to eliminate them), contaminations would be manifested as a one-sided variability in the scatter plot that both reduces the DoLP and increases the radiance for select observations. If correct, this hypothesis explains why a significant fraction of the scatter points in the visible bands are within error bars for both the radiance and the polarization (Figs. 4 and 5), while many are not.
For the 630 and 700 nm bands, the polarization differences between the model and the polarimeter are more extreme than the shorter wavelengths. While cloud contamination affects the longer wavelengths more severely, the occurrence of large polarization differences only in the bands with significant molecular absorption warrants special examination. Several issues must be considered.
First, light from wavelengths with large molecular absorption features have increased polarization when compared to adjacent bands that lack molecular absorption [25,26]. Therefore, overestimation of the molecular absorption will cause an overestimated DoLP in the model. The higher simulated DoLP (with respect to the observed quantity) may indicate that the molecular absorption included in the model is overestimated. For the 630 nm and 700 nm bands, the primary absorbing molecules are oxygen and water vapor, respectively. We expect that the MODTRAN oxygen model used is accurate since oxygen is a uniformly mixed and temporally consistent atmospheric gas. In contrast, water vapor is temporally variable. To account for this variability, we included AERONET-produced precipital water vapor (pwv) products into the MODTRAN model. We have compared pwv values retrieved by AERONET to values retrieved by a local SUOMINET station and found that the two instruments generally agree quite well. Therefore, we have no reason to suspect that the molecular absorption included in the model is overestimated.
Second, while we are confident in the ability of the SOS model to simulate situations with low molecular absorption, we are uncertain to what degree the model has been tested in spectral regions with high molecular absorption.
Third, the spectral-weighted average of the molecular optical depth that we use depends greatly on the accuracy of the filter transmission profiles and the accurate representation of the fine absorption features by MODTRAN. In these highly structured absorption complexes, small errors in the filter profiles or absorption features may cause errors in the weighted molecular optical depth and molecular SSA. These issues make interpretation of results in the absorption bands difficult.
Finally, polarization in these longer wavelength bands may be more sensitive to errors in the model aerosol parameters because the portion of the radiance coming from the aerosols as opposed to the molecules is higher compared to the shorter wavelengths. This effect results from both the higher molecular absorption in these bands and the lower Rayleigh optical depth at the longer wavelengths. Thus, enhanced differences in these bands could be the result of aerosol parameter errors. The potential for aerosol parameter errors becomes more apparent when the atmospheric conditions are considered. For all measurements taken in this study, the 500-nm aerosol optical depth ranged between 0.025 and 0.17. (In the absence of summer forest fires, Bozeman generally has a very clean atmosphere.) These low aerosol optical depths are in a range where AERONET radiance inversions encounter difficulties properly retrieving the aerosol parameters, especially the complex refractive index and single-scatter albedo . While the overall agreement of the comparisons here suggest that the retrieved parameters are at least reasonable in this aerosol optical depth range, we suspect that some biases may be introduced into the individual microphysical properties. (It is noted that the results were not significantly different if only retrievals with high sphericity (> 90%) were isolated for comparison.) Previous investigators have discussed conditions that may cause biases in the retrieved real refractive index [6,15,16]. Some of the comparison differences shown here may indicate that real refractive index biases exist in this AERONET data set. We test the possibility of this scenario in the next section.
3.4 Maximum DoLP comparisons with artificially increased real refractive index
While real refractive index biases are only one of several potential error sources, we investigated whether a refractive index bias could realistically account for the differences seen between the observations and the models. To test the sensitivity of the model to a potential bias, we introduced an artificial 5% increase to the AERONET real refractive index before calculating the aerosol scattering phase matrix and aerosol SSA included in the model. (Note that we continued to use the AERONET “direct sun” aerosol optical depths, so the model aerosol optical depth was not altered by this increase.) The magnitude of this increase was chosen arbitrarily. Figures 6 and 7 (which are similar to Figs. 4 and 5) show the results from the models with the artificially enhanced real refractive index when compared to the observed data.
For both the radiance and the polarization comparisons, the agreement between the observation and the model is much better with the real refractive index adjustment. The mean absolute DoLP difference over all data points improved from 0.047 to 0.02, while the mean absolute radiance difference improved from 8.5% to 5.4%. This agreement is also exhibited in the full sky images (not shown). While these results do not necessarily confirm a bias in the AERONET real refractive index for this data set–as other sources of error may exist–they do show that the possibility of a real refractive index error cannot be eliminated. They are also consistent with previous results which show (1) that polarization is very sensitive to changes in the real refractive index  and (2) that the intensity-only AERONET algorithm will sometimes underestimate the real refractive index for fine and mixed mode particles .
It is important to note that the better agreement obtained from artificially increasing the real refractive index is specific to this data set and should not be interpreted to apply to all AERONET data. Our purpose here is only to show the potential for a real refractive index bias. Also, further adjustments could be made to the real refractive index on a per wavelength basis until agreement is ideal, but manipulating the aerosol parameters to this degree would only show the sensitivity of polarization to real refractive index, not indicate the true real refractive index. Results from artificially increasing an isolated parameter (as done here) are not indicative of inversion behavior. Inversions retrieve all aerosol microphysical parameters (size distribution, sphericity, complex refractive index, etc.) simultaneously. An inversion that included the polarization with the radiance would most likely generate both size distributions and refractive indices that differed from radiance-only retrieved values for this data set. Therefore, our artificially adjusted real refractive index may be overcompensating for errors in other aerosol parameters and the exact value of our adjustment may not be meaningful.
We have shown polarization and radiance observations compared with results from radiative transfer model simulations which include aerosol parameters generated by AERONET. While the models generally agree well with the observations, some differences exist. Several potential error sources in the models were identified. Large molecular absorption features in some bands (630 and 700 nm) complicate the interpretation of the results. While several sources of error may exist, simulations suggest that the real part of the refractive index may be underestimated for the aerosol data set in question. This conclusion is not unwarranted given the low aerosol conditions over the course of the observations and the corresponding difficulties that these conditions pose to the AERONET inversion algorithm.
Recently, we moved the 630 and 700 nm polarimeter bands to 675 and 780 nm, respectively, to reduce the difficulties encountered with interpreting data in highly structured molecular absorption bands. In future studies, we should be able to better assess model vs. observation differences.
These results are consistent with previous results which have shown that the addition of polarimetric information to aerosol inversions better constrains the parameters, especially the retrieved real refractive index [5–8]. It is noted, however, that multiple scattering from sources outside the field of view (like clouds and the surface) will reduce the sky DoLP significantly . Out-of-field clouds could be problematic for almucantar retrievals that utilize polarization, because they reduce the sky polarization. This reduced polarization could be falsely interpreted as an artificially large aerosol real refractive index. In this study, the full sky polarimetric imager allowed us to select data where the full sky was completely free of clouds from horizon to horizon. A radiometer which only scans the almucantar and the principal plane would not allow the user this advantage. Therefore, it may be more vulnerable to these problems. Still, quality control algorithms (including almucantar symmetry tests) may be able to eliminate most of these problems. Furthermore, the imager method has its own inherit disadvantages as it requires a more complex calibration, and a second imager may be needed for the NIR wavelengths (which are needed for the inversion). Additional research in these areas is necessary.
Appendix 1. AERONET vs. polarimeter radiance comparisons
Both the AERONET CIMEL instrument and the polarimeter produce radiance data products. The polarimeter measures the full sky, while the CIMEL measures sky radiances in the solar almucantar and principal plane. The similarity of these radiance products provides an opportunity for an indirect calibration crosscheck. While direct comparisons can be made for the 450 and 500 nm bands of the two instruments, other bands can only be compared by interpolating the radiance between the bands. This approach is useful only if the inherent limitations of interpolation between spectra with molecular absorption bands are considered. In the following comparisons, the minimum principal plane radiances measured by CIMEL were interpolated to the polarimeter wavelengths and compared to the associated polarimeter radiance (Fig. 8 ). Because of the large oxygen absorption in the 630 nm band, the comparison at this wavelength should be taken cautiously. (For similar reasons, the 700 nm band, which is located in a water vapor band, is not shown.)
Considering that the two instruments are very different–one is a full sky imager and one is a photometer–and are calibrated with completely different standards, the achieved agreement is quite good. Since many calibration standards (including our own) struggle to output sufficient light at short visible wavelengths, we expect systematic errors in the calibration standard radiances to be most pronounced at these wavelengths. Differences seen at 450 nm may be attributable to these errors.
The authors would like to thank Maurice Herman and the Laboratoire d’Optique Atmosphérique (LOA) of Lille University for developing and maintaining the SOS scattering code , Oleg Dubovik and Tatyana Lapyonok for developing and maintaining the lookup tables of T-matrix kernels , and AERONET for providing both codes. We would like to thank Alexander Sinyuk for explaining the SOS input variables. This material is based on research sponsored by the Air Force Research Laboratory, under agreement numbers FA9550-07-1-0011 and FA9550-10-1-0115. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government.
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