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An all-sky imaging polarimeter was deployed in summer 2008 to the Mauna Loa Observatory in Hawaii to study clear-sky atmospheric skylight polarization. The imager operates in five wavebands in the visible and near infrared spectrum and has a fisheye lens for all-sky viewing. This paper describes the deployment and presents comparisons of the degree of skylight polarization observed to similar data observed by Coulson with a principal-plane scanning polarimeter in the late 1970s. In general, the results compared favorably to those of Coulson. In addition, we present quantitative results correlating a variation of the maximum degree of polarization over a range of 70-85% to fluctuation in underlying surface reflectance and upwelling radiance data from the GOES satellite.
©2011 Optical Society of America
Introduction
Skylight polarization in the visible and near-infrared (NIR) bands is an important physical quantity of interest in diverse areas of scientific research including atmospheric and climate studies and military sensing [1–6]. Skylight polarization varies with aerosols, clouds, and surface albedo, presenting a need for an instrument that can measure polarization over the entire sky dome rapidly enough to capture cloud motion. Previous studies of skylight polarization have used scanning polarized radiometers [7,8], cameras with polarizing filters looking down on a dome mirror [9], bore-sighted zenith-viewing film cameras with polarizing filters oriented at different angles [10], and a zenith-viewing digital imager with rotating polarizing filters [11,12]. To provide rapid, digital measurement of sky polarization over the full sky dome, we developed an all-sky imaging polarimeter based on a fisheye lens, liquid crystal variable retarders, and a CCD camera [1,2].
Several previous studies have revealed a qualitative correlation between diminished skylight polarization signatures and variable underlying upwelling radiation; however, beyond simulations that assume simple surface geometry, uniform aerosol distributions, and uniform underlying surface scattering conditions (see Fig. 4.23 in [8] and [12]), empirical and quantitative comparisons are not found with regularity. Prior studies include work by Coulson [8] at the Mauna Loa Observatory in which cloud cover beneath the observatory was estimated to range between 30 and 50% cloudy while clear overhead (these measurements made during the late 1970-early 1980s were done prior to the wide availability of satellite cloud cover data.) Shaw [13,14] found similar variability in polarization signature with unknown or unquantifiable surface properties during measurements of a total solar eclipse in 1973. These results and those of a second-order scattering simulation indicated many more orders of scattering were needed to capture what was observed. Finally, work done by Liu and Voss [12] indicated good qualitative agreement between a fluctuation of skylight polarization signatures and surface reflectance (e.g. over sea vs. land with different surface properties) as compared to simple scattering models factoring in surface reflectance.
To measure the effect of surface reflectance on observed skylight polarization patterns, the Montana State University all-sky imaging polarimeter was deployed to the Mauna Loa Observatory (MLO) in Hawaii during May and June 2008. This location allowed measurement of skylight polarization in an environment with historically minimal aerosol concentration at an elevation favoring few clouds overhead. These measurements, in conjunction with aerosol data available from the observatory and upwelling radiance data from satellite images, allowed for a comparison of skylight polarization with nominally consistent and minimal overhead aerosols and frequent clear overhead skies. The dark lava fields that surround the MLO also provide an opportunity to measure skylight polarization with low surface albedo. However, clouds often form below the observatory, greatly increasing the effective albedo of the “surface” below the MLO. This allowed a direct quantification of the influence of variable upwelling radiance and surface albedo on the observed polarization of the clear overhead sky devoid of significant aerosols.
1.1 Instrument overview
The Montana State University all-sky imaging polarimeter uses a 180° FOV (155° effective FOV during this deployment) equidistance-projection fisheye lens to image the sky dome through polarization optics onto a 1 Mpixel CCD camera [1]. Two liquid-crystal variable retarders (LCVRs) and an analyzing polarizer are used to obtain sequential images at different polarization states, which are then used to infer the Stokes parameters at each pixel using a system matrix inversion technique [3]. The 4-image sequence required to produce a complete Stokes vector image at a single wavelength can be obtained in less than 0.5 seconds. Five 10 nm-wide interference filters centered at 450, 490, 530, 630, and 700 nm are rotated into place using a filter wheel and data are taken iteratively for each band. An entire five-wavelength sequence, including time for filter wheel rotation and focusing, takes roughly 10-15 seconds. Rapid imaging at each wavelength was a driving requirement to accurately measure polarization in a partly cloudy sky and the LCVR design accomplishes this goal. The system is calibrated using an external rotating polarizer and an integrating sphere viewed at numerous angles to fully capture the system matrix of the imager over the field of view. Figure 1 illustrates the optical layout of the imaging system in the fisheye configuration. Shown also in Fig. 1 is the external sun occulter used to keep direct solar illumination from saturating the CCD array. Since the deployment discussed in this paper, the manual sun occulter has been replaced with a fully-automated sun occulting and temperature control system allowing for autonomous, all-weather deployment [14].
From the Stokes images, the degrees of both linear and circularly polarized light and the angle of polarization of the scattered light were calculated. The angle of polarization is a useful quantity in determining the location of the polarization neutral points in the atmosphere. The location and presence of these points are useful indicators of atmospheric aerosol variability [8]. The focus of discussion in this paper will be the degree of linear polarization (DoLP), or the fraction of scattered light from atmospheric constituents that is linearly polarized. Circular or elliptically polarized light observed from atmospheric scattering is generally negligible [15] and thus monitoring of this quantity was only used to assure that the instrument was functioning properly (if this component exceeded 3%, the instrument calibration was checked and recalibrated if needed). The DoLP, per pixel, is calculated from the Stokes images as shown in Eq. (1).
1.2 Atmospheric polarization
Atmospheric polarization signatures originate from two primary mechanisms. The first, single scattering by gas molecules and small particulates, is explained using Mie scattering theory for which Rayleigh theory is the small-particle limit [16,17]. The second process that affects polarization signatures is the multiple scattering of light in the atmosphere from clouds, aerosols, and the surface. Multiple scattering contributes to the depolarization of the sky and in practice adds a level of complexity to theory that is difficult to quantify in the context of all scattering objects in a given atmospheric scene. Most current polarized radiative transfer codes only account for a uniform underlying surface and thus are limited in their ability to accurately explain the variable scenes observed in typical measurements.
For this paper, the main focus is how the sky DoLP is affected by changes in the underlying clouds beneath the imaging system, as these clouds provided significant upwelling radiance. Rayleigh scattering theory dictates that scattered radiant intensity will have maximum DoLP at angles orthogonal to the illumination source, in this case, the sun [16]. Use of an all-sky fisheye lens allows imaging of the full arc of maximum DoLP at a scattering angle α (as defined in Fig. 2 ) of 90° that moves from the zenith at sunrise to the horizon at midday and then back to the zenith in the afternoon. The scattering geometry for the principal scattering plane encompassing the sun, observer and scatter (P) is shown in Fig. 2. Note that because the sun is effectively at infinity, the unit vector direction n^s from the scattering volume P is identical to that of the unit vector direction from the observer location.
The actual amount of linear polarization seen in the real atmosphere differs from pure Rayleigh single scattering predictions (a maximum of ~94% linearly polarized [16]). Equation (2) shows the relationship between scattering angle, the molecular depolarization parameter δ = 0.031 [16], introduced to account for the molecular asymmetry seen in common atmospheric molecules, and the maximum DoLP observed in the principal plane (PP).
Furthermore, scattering by clouds and aerosols and reflected radiance from the ground increases the amount of unpolarized light (s0) entering the field of view of the imager, which decreases the maximum atmospheric DoLP. To quantify the complicated relationships between these variables, the polarimeter has been deployed at Montana State University in Bozeman, MT, and at the NOAA Mauna Loa Observatory (MLO) on the island of Hawaii. In Bozeman deployments, the polarization data were complemented with data from a suite of supporting instruments that include a co-located weather station, scanning solar radiometer, infrared cloud imager, and cloud lidar. The summer 2008 MLO deployment provided critical clear-sky data (closer to Rayleigh conditions) used to both validate the calibration of the instrument [1] and to compare results to previous similar skylight polarization measurements.
2. Mauna Loa Observatory
The Mauna Loa Observatory (MLO) has historically been a site in which cloud-free, low-aerosol sky measurements have been made [7,8]. In the late 1970s and early 1980s, K. Coulson initiated a measurement campaign with a scanning zenith slice polarimeter to obtain a cross section of the degree of polarization over a narrow sun-zenith-observer slice (principal plane) of the sky dome. MLO was a favored location owing to its elevation of 3,394 m above sea level and typically low optical thicknesses and infrequent cloud presence above the observatory. Clouds and aerosols tend to remain beneath the observatory until the late morning, only rising to the observatory level on some days in early to mid-afternoon as the local heating of the surrounding volcanic landscape shifts the downslope winds upward, carrying clouds and aerosols with them. Furthermore, the surrounding surfaces near the observatory have little or no vegetation and are primarily volcanic lava flows with dark colorations. Albedo from the sea surface accounted for 4-5% of total reflectance and contributions to depolarization were minimal owing to the centralized observatory location on the island [8]. This made for a very low reflectivity and reduced scattering from ground surfaces entering into the FOV of the imager. For these reasons, and due to the in situ ability to quantify the aerosol changes throughout the day, MLO was chosen as an ideal location to observe a nearly Rayleigh atmosphere.
During the summer 2008 deployment, however, an increase of volcanic activity at nearby Kilauea resulting in significant gaseous plumes, combined with the southwesterly trade winds, led to an increased and variable presence of clouds and aerosols beneath the observatory. The result of the significant underlying cloud cover was that light scattered from the tops of these clouds, while being beneath the observatory, contributed to an increase in multiple scattering which led to significant non-Rayleigh polarization signatures. Figure 3 shows an illustration of the scattering process leading to skylight depolarization. It is stressed that overhead total optical thickness measurements obtained during the 2008 deployment indicated extremely minor aerosol presence and rarely exceeded a few hundredths above the expected Rayleigh optical thickness.
3. Measurements and results
3.1 Measurements
The imager was deployed at MLO from 21 May 2008 to 3 June 2008 and operated continuously throughout the day from sunrise until sunset. Images such as those in Fig. 4a (for 700 nm) were produced on 1-2 minute intervals for each of the five wavelengths. In this early morning image with clear sky overhead, we see the characteristic maximum DoLP arc stretch across the sky with flaring at the edges caused by the fisheye lens. The sun, not in the FOV of the imager at this time, moves across the sky from left to right, translating the arc position throughout the day. Figure 4b shows the mapping of the effective scattering angle α to the fisheye reference plane. Note how the black contour at 90° correlates well with the maximum DoLP band in the left image.
Fig. 4 (a) DoLP image at 700 nm of a clear early morning (23 May 2008) just after sunrise, at around 0620 Hawaiian Standard Time (HST, UTC −10) with the sun to the east. (b) The scattering angle (with respect to the sun) mapped to the fisheye lens image plane.
3.2 Comparisons to previous data at MLO
Coulson [8] deployed a scanning zenith-slice polarized radiometer that scanned across the solar principal plane (or sun’s vertical) in 5° increments. Operating in dual-polarization-channel mode at eight wavelengths from 320 to 800 nm, this system was capable of completing a zenith scan for all eight wavelengths every 24 minutes. For the majority of the published results, data were taken in the morning, typically with solar zenith angles not less than 20⌡. The morning was preferred by Coulson under the premise that in the afternoon solar heating caused aerosols and orographic clouds to frequently climb to and above the observatory level, thereby obscuring and depolarizing further the observable skylight through multiple scattering processes. Similar cloud motion was observed during our deployment; however, it only occurred on 2-3 days during the roughly two-week campaign at the observatory (data from those days are not included in the analysis shown here).
For comparing the all-sky imaging data to Coulson’s, the DoLP images were processed to locate the principal plane in each image and a slice was extracted from the image for the appropriate range of scattering angles. Localized averaging over a 3x3 pixel area near the maximum in the principal plane was used to produce a profile of maximum DoLP versus solar elevation angle, which was then compared to Coulson’s data. Figure 5 reproduces the original Coulson results in the principal plane. All dotted and dashed lines refer to data taken in 1977 by Coulson at 800 and 365 nm. Data taken with the MSU imager are shown with solid lines and were taken at the closest wavelengths to those data of Coulson at 700 and 450 nm. Coulson repeatedly states that the data on 19 February 1977 represents the clearest sky conditions, both above and below the observatory, in 30 years of prior measurements. As a result, the maximum DoLP for that day is consistently above 80%. Note that while Rayleigh single scattering predicts a maximum DoLP of ~94%, 85% is a commonly observed maximum near sunrise. Multiple scattering from molecules, aerosols, clouds, and the surface and minimal residual aerosol single scattering contribute to this overall depolarization [8].
Fig. 5 Morning data of Coulson (- -) for 800 and 365 nm wavelengths compared to 2008 imager data (-) at 700 and 450 nm.
The wavelength dependence of the maximum DoLP is shown in Fig. 6 . Imager data, although at different wavelengths (700 and 800 nm, respectively) than data taken in 1977, occur on a relatively flat section of the DoLP wavelength dependence curve and match well in structure and variation. The Coulson data at 365 nm, however, are more depolarized than the imager data at the minimum wavelength of 450 nm. This is expected because of the rapid decline of DoLP as wavelength trends toward the ultraviolet. This trend is further illustrated in Fig. 6 which shows the DoLP dependence vs. wavelength.
Fig. 6 Comparisons between Coulson (- -) and 2008 MSU imager data (-) for very clear, mostly clear, and dust storm conditions.
In Fig. 6, as in Fig. 5, all Coulson data are shown as dashed lines, and the solid lines indicate the average over nine 2008 mornings of clear days (no encroaching clouds near the observatory) at each of the 5 wavelengths for the same AM solar elevation angles. Also shown in Fig. 6 are four Coulson data points corresponding to the average of 2 days of mostly clear data at 365 and 800 nm [8] which closely resemble conditions during the 2008 study. Furthermore, the dashed red line in Fig. 6 is Coulson data taken during an incursion of Asian dust and is shown as a rough boundary for what might be expected for the maximum DoLP when non-Rayleigh, aerosol-laden conditions exist overhead.
The clear data from 19 February 1977 [8] illustrate little spectral dependence across wavelengths above 500 nm. For 450 nm and lower, however, the maximum DoLP drops significantly as scattering—and therefore multiple scattering—increases. This falloff explains the difference in DoLP principal plane signature in Fig. 5 when comparing the 365 to 450 nm data. Data collected in 2008, although more coarsely sampled in wavelength than Coulson’s data, were not statistically different across the spectral band. The error bars represent a 1-σ standard deviation of averages over nine days (two in the case of Coulson data) of data taken within ± 1° of the specified solar elevation. The magnitudes of the two very clear days taken in 1977, however, differ from 2008 data much like the trend seen in Fig. 5, with the maximum DoLP lower for our data relative to Coulson’s, as the underlying cloud clarity was much different than the cited Coulson data. Therefore, the averages over the 2 mostly clear days at 10° and 45° solar elevation angle in 1977 are shown with corresponding standard deviations for comparison. As can be observed, these 1977 averages, when compared to the average 2008 data, compare favorably if the wavelength dependence is extrapolated.
As seen from these figures, comparisons between Coulson’s 1977 data and those taken in 2008 with the imager are favorable. Qualitative estimates from Coulson at between 30 and 50% underlying clouds [8] on the two mostly-clear days (9 and 10 March 1977) compare well with estimates from GOES satellite imagery of between 5 and 30% cover over the mostly clear days in 2008 and the comparison of DoLP averages from these times shown in Fig. 6 are consistent.
3.3 Polarization and upwelling radiance
As implied by these results, it was also found that it was not the aerosol optical depth (AOD) that most influenced the overall depolarization of skylight at the MLO. Reflected radiance of the underlying clouds beneath the observatory appear to have contributed more to a reduction in the DoLP for days of consistently low AOD. Figure 7 illustrates this for two days that were very clear overhead, for which the overhead AOD at 700 nm was consistently near 0.03 ± 0.001 throughout the day. The top row shows two 700 nm DoLP images taken on different days at 1000 Hawaiian Standard Time (HST, UTC-10). Beneath the sky polarization images are two images of upward-reflected radiance taken from the GOES-11 satellite stationed over the western United States and Pacific Ocean at the same time (1000 HST = 0000 UTC) [18,19]. Note that the all-sky polarization images are realigned so that west is to the left and east to the right, to match the downward-looking perspective of the satellite images.
Fig. 7 A comparison of 700 nm DoLP images to GOES albedo imagery taken at 1000 HST (UTC −10). Instrument deployment location is denoted by ‘x.’ The small disc in the top images is the sun occulter. The all-sky polarization images have been flipped to match the down-looking perspective of the satellite images.
The GOES reflected radiance images revealed that even though overhead optical depth was consistently low on these two days, the radiances reflected into the sky were very different. While both GOES images show the cloud bank that had formed on the south to southwest side of the island (primarily due to the Kilauea eruption), the rest of the scene is largely cloud-free for 23 May 2008. By contrast, there are significant additional clouds present on 3 June 2008. As a result, the overall DoLP observed for 23 May was greater than that observed on 3 June due to the increased depolarization introduced by the increased upwelling unpolarized light from the clouds. Furthermore, clustering of clouds near the southern end of the island creates a north–south asymmetry in the polarization images, with slightly lower polarization in the southern sky relative to the northern sky.
Looking to Fig. 8 , which shows the maximum DoLP values extracted from the principal plane profile over the course of the day, the depolarization effects are especially visible for the morning hours—when the atmosphere around MLO is the least turbid for the two days in question. However, this figure illustrates an additional effect not reported by Coulson since his polarimeter operated predominantly in the morning hours. Owing to the proximity of the 2008 measurements to the summer solstice, the solar track through the day passed nearly exactly overhead from east to west, with the sun passing within a degree of the zenith. As such, the maximum DoLP profile was expected to be roughly symmetrical from morning to evening. However, it is apparent that additional effects were reducing the afternoon maximum DoLP. Completely explaining the observed signatures would require accounting for the variable solar position, the unknown bidirectional reflectance distribution function (BRDF) of the island’s surface, and changing cloud distributions. This would require a full three-dimensional polarized radiative transfer model that would have computational requirements and such specific input requirements that it would be nearly impossible to replicate the measurements. Nevertheless, section 3.4 shows that the regression of the maximum DoLP with upwelling radiance reproduces the asymmetric trend of the plots in Fig. 8, thereby indicating that a primary driver of this asymmetry is the temporal variation of clouds below the observatory.
3.4 Regression analysis
To better understand the observed results, the maximum DoLP was compared to the upwelling radiance derived from the GOES visible band data using both pre and post-launch calibration information [18,19]. Localized radiance averages over the extent of the island were calculated to yield mean radiance values to quantitatively compare to the maximum DoLP at corresponding times. Because clouds tend to form inland and close to the island, and because the albedo of the surrounding ocean is low and consistent in comparison to that of the variable clouds [8], the rough extent of the island—a radius of 50 km from MLO—was chosen as the area to average the radiance. It should be noted that the selection of this averaging range is a unique characteristic of the island setting and that it reflects the radial extent where the maximum variation of average radiance was observed.
The second quantity derived from GOES data was a reflectance that corrects for solar zenith angle variation over the course of the day, termed the isotropic albedo [20]. Useful for identifying clouds that are present over a relatively consistent and localized surface area, this data product was used to remove the effects of constant surface-reflected radiance [20]. The main drawback of using this metric is that the inherent BRDF of the cloud and ground reflective properties are ignored and the surface is assumed to be a Lambertian reflective surface. Again, because the exact surface properties are not known, this is the only approximation that can be made in this situation [21].
An equation can be developed for the isotropic albedo ρiso by beginning with an expression for the solar spectral irradiance E (W m−2 μm−1) incident on the surface from exo-atmospheric spectral irradiance E 0 with the Sun at zenith angle θ z:
where d m is the mean Earth-Sun distance and d is the Earth-Sun distance at the time of the measurement. The assumed Lambertian surface reflects spectral radiance L (W m−2 sr−1 μm−1) given by
so that the isotropic albedo ρiso can be written as
To capture the variability across the island, the isotropic albedo was averaged over the extent of the island using a single mean zenith angle because of the small variation in solar zenith angle across the island for a single observation. The resulting average isotropic albedo expression is
where the average isotropic albedo is found from the mean of the radiance L multiplied by the secant of the mean solar zenith angle θz, over N × M latitude and longitudinal pixels covering a radial distance 50 km from MLO. Both L n,m and E 0 have inherent detector spectral response functions that cancel in the ratio. The ratio of π/Eo was determined a priori using tables of solar irradiance measurements across the GOES bandwidth from 530 to 790 nm; thus the only unknown L is obtained from GOES measurements [22]. The ratio of d to dm is nominally near 1 and varies by only approximately 1% over the course of the 2-week MLO deployment.
During this deployment the optical depth of the overhead sky did not vary significantly and remained negligibly low, so the data were modeled with a combined multivariate regression using a linear isotropic albedo term and a decreasing exponential upwelling radiance term. A series of Monte Carlo iterations were performed on the regression taking the form of Eq. (7), which shows the equation used for the empirical fit of the estimated degree of linear polarization DOLPest with coefficients bn, isotropic albedo ρ iso and radiance L.
This equation can be used to predict the maximum sky DoLP for a given value of isotropic albedo , for which the corresponding upwelling radiance can be found from
Figure 9a shows a single Monte Carlo fit of the maximum DoLP data to only the upwelling radiance in red, and the improved model with the linear isotropic albedo term in green. Figure 9b shows the full 3-D regression space with isotropic albedo and radiance on the x and y axes and DoLP on the z axis, illustrating the spread in isotropic albedo given a fixed radiance. For the data in Fig. 9, four of the nine clear-sky days were chosen randomly to fit to Eq. (7) and then the remaining 5 days of data were then used with that model to generate an estimate of the DoLP given the radiance and isotropic albedo for those days. Note that adding the linear isotropic albedo term to the regression produces a model that better matches the spread observed in the data for a given radiance (Fig. 9a, green and blue). Figure 9c shows the distribution of the residuals for this fit. Standard deviations of the residuals for all wavelengths were less than 0.02, or roughly 2% variation in DoLP.
Fig. 9 a) Single and multivariate regression of GOES measured upwelling radiance to 450 nm DoLP. b) Multivariate regression with added isotropic albedo term shown in 3-D. c) DoLP residual histogram for given fit at all wavelengths.
There are several reasons for the observed spread in DoLP for a given upwelling radiance value. First, for a fixed upwelling radiance, there may be different albedo values, each with its associated solar zenith angle, that produce the same upwelling radiance. This means that different solar and viewing geometries can have the same upwelling radiance, but likely with different DoLPs for the different geometries. It is to compensate for this spread that the isotropic albedo was added as a variable to the regression. However, the isotropic albedo cannot account fully for these geometry effects because in reality the island and clouds have unique and unknown BRDFs. Second, using averages of radiance or albedo ignores the inevitable spatial and geometric variability. In essence, this analysis assumes a homogenous and Lambertian surface surrounding the observatory and, as observed in GOES data, this is not the case. However, the addition of the albedo to the regression does account for a sizable fraction of the spread of DoLP for a fixed radiance (seen in the green multivariate regression model in Fig. 9a).
Overall, the fit to Eq. (7) was repeated for 1000 Monte Carlo combinations of a randomly selected four of the nine totally clear (overhead) days observed during the deployment. This selection was done with replacement such that the fit might contain the same day multiple times. Each fit was then evaluated with the remaining five days not used in the fit. The green and blue lines in Fig. 10 show the 700 nm data presented originally in Fig. 8, along with six red lines that represent six DoLP model profiles created with coefficients generated from randomly selected Monte Carlo trials. These results indicate that the model generally reproduces the asymmetry observed in the DoLP during mornings and afternoons.
The overall average residuals over Monte Carlo trials from these fits were similar to those shown in Fig. 9c. The average of the 1000 Monte Carlo fit coefficients and standard deviations are listed in Table 1 . Of these coefficients, only the b1 term varied significantly from a Gaussian distribution. Several fits had very small b1 values near zero, while the majority had values near −0.1.
Table 1. Average Fit Coefficients with Standard Deviations
To evaluate the consistency of these model results, the entire nine-day data set was modeled using the average fit coefficients shown in Table 1. Figure 11 illustrates the results with scatterplots of the measured and modeled data for all wavelengths using all 9 clear days from the deployment. All observed data agree well with the predicted counterparts, with R-squared values of 0.83 or higher for all wavelengths.
Fig. 11 Scatterplots of predicted vs. observed DoLP using the multivariate regression of upwelling radiance and isotropic albedo with the average coefficients shown in Table 1.
For further comparisons, the observed data were compared to a successive order-of-scattering (SOS) radiative transfer code model derived from [15]. This model is a polarized radiative transfer code that accounts for upwelling radiance assuming a uniform underlying Lambertian surface, with the atmosphere divided into a series of plane-parallel layers. In this simulation, the solar zenith angle was varied over the hemisphere from 0° to 80° of zenith angle and the surface reflectance was varied from 0.1 to unity.
These results indicate that, while a simple Lambertian surface reflectance model is not sufficient to replicate the measurements exactly, the trends indicate that there is a significant relationship between the three variables. Figure 12 shows the 450-nm observed maximum DoLP data plotted against upwelling radiance, along with the corresponding curves produced by the polarized radiative transfer code for isotropic surface reflectances of 0.1 (green) and 0.2 (red). Generally, as surface reflectance increases, the maximum DoLP decreases as the upwelling radiance increases. Only for locations on the curves with large solar zenith angles (far left points on the curves) do these curves converge, and as solar zenith angle decreases (approaching normal incidence) these curves diverge, as more surface reflectance gives rise to more upwelling radiance (right points on the curves). These results indicate that, while not ideal, an isotropic surface varying from 0.1 to 0.2 roughly describes the bounds of what could be expected from clear-sky polarized radiance measurements at MLO.
Fig. 12 Comparison of observed DoLP vs. upwelling radiance and theoretical predictions from a SOS plane-parallel Mie scattering code.
4. Conclusions
This paper has presented results from a 2008 deployment to the Mauna Loa Observatory to measure the polarization of the sky dome. Work done by Coulson has been independently verified and expanded upon. GOES satellite measurements have been used to empirically correlate upwelling radiance and surface reflectivity with the degree of linear polarization. It was found that the underlying spatial distribution and variability of surface scattering from clouds—both natural and volcanic—were the dominant drivers in fluctuations in the DoLP over the course of 2 weeks of observations and that polarized radiative transfer codes consistently predict fluctuations of polarization signature as the underlying reflection varies. A regression model is provided, which generally reproduces the observed polarization trends, including morning-afternoon asymmetry.
Acknowledgments
We gratefully acknowledge Dr. John Barnes, Director of the NOAA Mauna Loa Observatory (MLO), and the MLO staff, for allowing us access to the observatory, helping with the deployment, and helping to obtain and understand the different observatory aerosol products. We also thank two reviewers whose comments significantly improved the manuscript. 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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