Comparison of full-sky polarization and radiance observations to radiative transfer simulations...

Comparison of full-sky polarization and

radiance observations to radiative transfer

simulations which employ AERONET products

Nathan J. Pust,* Andrew R. Dahlberg, Michael J. Thomas, Joseph A. Shaw

Department of Electrical and Computer Engineering, 610 Cobleigh Hall,

Montana State University, Bozeman, Montana 59717, USA *[email protected]

Abstract: 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 Optical Society of America

OCIS codes: (110.5405) Polarimetric imaging; (010.1310) Atmospheric scattering; (010.5620)

Radiative transfer; (010.1110) Aerosols.

References and links

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#149825 - $15.00 USD Received 24 Jun 2011; revised 1 Aug 2011; accepted 2 Aug 2011; published 8 Sep 2011(C) 2011 OSA 12 September 2011 / Vol. 19, No. 19 / OPTICS EXPRESS 18602

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1. Introduction

Over the last decade, important progress has been made toward a better understanding of the

radiative effects of aerosols on climate [1]. To develop a more accurate aerosol climatology,

several surface-based [2] and satellite-based optical remote sensing platforms (e.g. [3] and

[4]) 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 [8]. 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 [13] which uses aerosol products

from the Aerosol Robotic Network (AERONET) [2]. 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.

1.2 AERONET

The Aerosol Robotic Network (AERONET) of solar radiometers measures direct solar

irradiance and sky radiance across the globe [2]. 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 [14]. 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 [13] used in this study has

been used extensively by previous investigators (e.g [15–17].) and has been compared

successfully to other models [18]. 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).


Instrument Calculation Parameter

AERONET

Radiance Polarization

SOS Model

AERONET

Inversion

Size distribution

Refractive index

Radiance PolarizationRadiance

MSU Polarimeter

Mie Code

T-matrix Table

Scattering phase

matrix

Molecular

Optical Depth

MISR

Surface albedo

BRF

Sun zenith angle

Aerosol

Optical Depth

Aerosol

single scatter albedo

MODTRAN

Molecular

single scatter albedo

Fig. 1. Overview of the radiance and polarization comparison methodology.

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 [16] 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%.

10-1

100

101

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02AERONET retrieved volume size distribution

Particle radius (um)

dV

/dln

r (u

m3/u

m2)

0.4 0.6 0.8 11.4

1.45

1.5

1.55

1.6AERONET retrieved refractive index

Wavelength (um)

Re

al In

de

x

0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

Wavelength (um)

Ima

gin

ary

In

de

x

10 Jul 2009

22 Jul 2009

28 Aug 2009

02 Sep 2009

23 Sep 2009

24 Sep 2009

27 Sep 2009

Fig. 2. Representative sample of aerosol retrievals for all study days.

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 [20]

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 [21].

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 [22]. MISR provides BRF parameters for a modified

version of the RPV (Rahman-Pinty-Verstraete) model [23]. (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 [24]. Since the area surrounding Bozeman is largely forested, we tried the

“high NDVI forest” parameters specified in the table on pg. 1715 of [24], but the model

results were not significantly different from the case where a completely unpolarized surface

was defined.

Fig. 3. Excerpt from a time lapse (Media 1) of observation and model comparisons for 02 Sept

2009, Bozeman, Montana, USA. The RGB composite images were formed from the 450, 530,

and 630 nm images. Error and degree of linear polarization (DoLP) images are shown only for

the 450 nm band. Radiance error is defined as (observed - modeled)/observed. The arc with a

centered-disk is an automated sun occulter. The Babinet (above the sun) and Brewster (below

the sun) neutral points are seen in both the observed and modeled DoLP.


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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.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Polarimeter

SO

S M

ode

l

Maximum DoLP: 450 nm

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Polarimeter

SO

S M

ode

lMaximum DoLP: 490 nm

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Polarimeter

SO

S M

od

el


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Polarimeter

SO

S M

od

el


Fig. 4. Comparison of the observation and model maximum degree of polarization (DoLP) for

times when the polarimeter measurement and AERONET retrieval were within 10 minutes of

each other. 530 nm results (not shown) are very similar to the 450 and 490 nm results.

Polarimeter error bars are shown which vary from ± 0.03 for fully polarized light to ± 0.003 for

unpolarized light.

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


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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 [11]. A more critical analysis of potential error sources follows.

0 2 4 60

2

4

6

Polarimeter

SO

S M

odel

Minimum Sky Radiance: 450 nm

0 2 4 60

2

4

6

Polarimeter

SO

S M

odel


0 2 4 60

2

4

6

Polarimeter

SO

S M

od

el


0 2 4 60

2

4

6

Polarimeter

SO

S M

od

el


Fig. 5. Same as Fig. 4 but for minimum sky radiance. Radiance units are uW/(cm2*Sr). Since

radiance errors are not characterized for the polarimeter and the polarimeter is calibrated with a

similar method to the AERONET radiometers, error bars that reflect the ± 5% error advertised

by AERONET [14] are shown for reference.

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 [27]. 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.


0 0.2 0.4 0.6 0.8 10

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0 0.2 0.4 0.6 0.8 10

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0 0.2 0.4 0.6 0.8 10

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Fig. 6. Same as results from Fig. 4, but for models with the AERONET real refractive index

artificially increased by 5%.

0 2 4 60

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0 2 4 60

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Fig. 7. Same as results from Fig. 5, but for models with the AERONET real refractive index

artificially increased by 5%.

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 [8] and (2) that the intensity-only AERONET algorithm will

sometimes underestimate the real refractive index for fine and mixed mode particles [6].


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.

4. Conclusion

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 [21]. 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.

0 2 4 60

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Fig. 8. Comparisons of minimum radiance measured in the principal plane by the polarimeter

and the AERONET CIMEL. Radiance units are uW/(cm2*Sr). Error bars reflect the ± 5% error

advertised by AERONET [14]. 700 nm is not shown but shows similar results to the other

wavelengths. Only data for which the two instruments took measurements within 10 minutes of

each other are shown.

Acknowledgments

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 [13], Oleg Dubovik and Tatyana Lapyonok for developing and maintaining the lookup

tables of T-matrix kernels [16], 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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