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  • View in gallery

    (left) SHEBA mosaic (original) image 4653 × 5687 pixels with a pixel size of 2.0 m, (top right) subset of the original image 500 × 500 pixels, and (bottom right) segmented subset of the original image. Red dots on the original image show locations of the subset image, and red dots on the subset images show the area used for the simulations that follow. Open water areas are shown in blue, and melt ponds are depicted in turquoise.

  • View in gallery

    Simulated albedo as measured from the UAV flying across leads (a) 200, (b) 400, (c) 800, and (d) 1600 m. Areas of low reflectance: open water with Fresnel reflection; areas of high reflectance: sea ice with an albedo of 0.75.

  • View in gallery

    Downwelling irradiance over the idealized sea ice leads of Fig. 2, having width (left) 800 and (right) 1600 m. Irradiance is relative to F0cosθ0 = 1.0 at the top of the atmosphere, where F0 is the extraterrestrial solar irradiance at 550 nm and θ0 is the solar zenith angle.

  • View in gallery

    (top left) Upwelling irradiance, (top right) downwelling irradiance, (bottom left) albedo, and (bottom right) net flux averaged along a horizontal flight track from one side of Fig. 2’s cell to the other. Leads 200 m [red; (a) in Fig. 2], 400 m [blue; (b) in Fig. 2], 800 m [green; (c) in Fig. 2], and 1600 m [gray; (d) in Fig. 2].

  • View in gallery

    Simulated albedo as measured from the UAV flying above the image subset shown in Fig. 1 at altitudes (a) 10, (b) 20, (c) 50, and (d) 100 m. Areas of low reflectance: open water with Fresnel reflection; areas of high reflectance: sea ice with an albedo of 0.75. Note the scale change in the legend between the top and bottom panels.

  • View in gallery

    As in Fig. 4, but for above a point exactly in the middle of the 500 × 500 pixel subset of Fig. 1, above a melt pond, for varying τc: 3.3 (gray), 7.7 (blue), 9.0 (green), 12.1 (black), and 9.0 with aerosol (red); θ0 = 60°.

  • View in gallery

    As in Fig. 6, but for τc = 9.0 and Lambertian surface (black), BRDF for sea ice surface (blue), and Lambertian surface with aerosol (red); θ0 = 60°.

  • View in gallery

    As in Fig. 6, but for above a point exactly 100 pixels to the left of the central point considered in Fig. 7, above a triangular section of open water.

  • View in gallery

    As in Fig. 8, but for τc = 9.0, Lambertian surface, and aerosol uniformly distributed below cloud, for wavelengths 550 (green) and 380 nm (violet); θ0 = 60°.

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Monte Carlo Study of UAV-Measurable Albedo over Arctic Sea Ice

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  • 1 Arctic Research and Consulting, San Diego, California
  • 2 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
  • 3 Dartmouth University, Hanover, New Hampshire
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Abstract

In anticipation that unmanned aerial vehicles (UAVs) will have a useful role in atmospheric energy budget studies over sea ice, a Monte Carlo model is used to investigate three-dimensional radiative transfer over a highly inhomogeneous surface albedo involving open water, sea ice, and melt ponds. The model simulates the spatial variability in 550-nm downwelling irradiance and albedo that a UAV would measure above this surface and underneath an optically thick, horizontally homogeneous cloud. At flight altitudes higher than 100 m above the surface, an airborne radiometer will sample irradiances that are greatly smoothed horizontally as a result of photon multiple reflection. If one is interested in sampling the local energy budget contrasts between specific surface types, then the UAV must fly at a low altitude, typically within 20 m of the surface. Spatial upwelling irradiance variability in larger open water features, on the order of 1000 m wide, will remain apparent as high as 500 m above the surface. To fully investigate the impact of surface feature variability on the energy budget of the lower troposphere ice–ocean system, a UAV needs to fly at a variety of altitudes to determine how individual features contribute to the area-average albedo.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dan Lubin, dlubin@ucsd.edu

Abstract

In anticipation that unmanned aerial vehicles (UAVs) will have a useful role in atmospheric energy budget studies over sea ice, a Monte Carlo model is used to investigate three-dimensional radiative transfer over a highly inhomogeneous surface albedo involving open water, sea ice, and melt ponds. The model simulates the spatial variability in 550-nm downwelling irradiance and albedo that a UAV would measure above this surface and underneath an optically thick, horizontally homogeneous cloud. At flight altitudes higher than 100 m above the surface, an airborne radiometer will sample irradiances that are greatly smoothed horizontally as a result of photon multiple reflection. If one is interested in sampling the local energy budget contrasts between specific surface types, then the UAV must fly at a low altitude, typically within 20 m of the surface. Spatial upwelling irradiance variability in larger open water features, on the order of 1000 m wide, will remain apparent as high as 500 m above the surface. To fully investigate the impact of surface feature variability on the energy budget of the lower troposphere ice–ocean system, a UAV needs to fly at a variety of altitudes to determine how individual features contribute to the area-average albedo.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dan Lubin, dlubin@ucsd.edu

1. Introduction

The remoteness and harsh environment of polar regions have recently motivated innovative and effective use of unmanned aerial vehicles (UAVs) for studies of atmospheric science, sea ice, and climate change. Inoue et al. (2008) used Aerosonde UAVs to map melt pond fraction on Arctic sea ice, and Tschudi et al. (2008) used these measurements to test satellite retrievals of melt pond coverage. Similarly, Aerosondes have been successfully used in wintertime boundary layer energy and moisture flux studies over Antarctic polynyas (Cassano et al. 2010). During the Mixed-Phase Arctic Cloud Experiment (MPACE; Verlinde et al. 2007), an Aerosonde provided thermodynamic and aerosol data in support of cloud microphysical observations (Morrison et al. 2008). Bates et al. (2013) measured tropospheric aerosol number concentrations and light absorption coefficients using a small UAV (wingspan: 2.7 m) above Svalbard, Norway. With the availability of larger UAVs, such as the NASA Sensor Integrated Environmental Remote Research Aircraft (SIERRA), payloads have expanded in capability to include lidar for sea ice freeboard measurement (Crocker et al. 2012). UAVs have been used to study the CO2 flux of cryoconite across an Arctic glacier ecosystem (Hodson et al. 2007). At tropical and midlatitudes, there has been considerable progress in atmospheric radiation measurement using UAVs, including multiple aircraft in stacked formation (Roberts et al. 2008). The capability to measure atmospheric radiation simultaneously with aerosol and thermodynamic properties is improving with newer aircraft, such as the University of Colorado’s Pilatus UAV (de Boer et al. 2016).

We can therefore anticipate that polar regions will soon see UAV-based atmospheric radiation budget studies, given the prior success with sea ice research and the need to quantify the atmospheric energy budget for understanding sea ice evolution (Perovich et al. 2008). One recent example using a major NASA C-130 research aircraft is the Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE; Smith et al. 2017), which combined shortwave and longwave radiation and cloud microphysical measurements with observations of sea ice type, fraction, and freeboard in the marginal ice zone during the critical late-summer transition from minimum sea ice extent to refreezing. Polar radiation and cloud microphysical measurements have also been successfully made using a tethered balloon (Lawson et al. 2011). Miniaturization of these types of payloads for deployment with increasingly capable UAVs can be expected to make important contributions throughout the high Arctic.

In anticipation that UAVs may have a useful role in atmospheric energy budget studies over sea ice, we consider three-dimensional (3D) radiative transfer over a highly inhomogeneous surface involving open water, sea ice, and melt ponds. Most atmospheric research using Monte Carlo (MC) techniques has focused on their utility for 3D cloud configurations (e.g., Marshak and Davis 2005). In polar regions MC methods are also appropriate for radiative transfer studies over spatially inhomogeneous surfaces. Our prior work using an MC simulation has shown how multiple reflection of photons between a high-albedo surface and a cloud base enhances downwelling shortwave irradiance over adjacent open water (Podgorny and Lubin 1998). These simulations were found to be realistic in a surface-based radiation measurement field program at Palmer Station, Antarctica (Lubin et al. 2002; McComiskey et al. 2006).

In this study, we consider how 3D radiative transfer effects might affect UAV-based radiation measurements. As in Podgorny and Lubin (1998), we consider simplified cloud geometry and spatial variability over a horizontally inhomogeneous surface. When comparing the theoretical MC results of Podgorny and Lubin (1998) with Antarctic field data (Lubin et al. 2002; McComiskey et al. 2006), we found that the overall predicted effect of horizontal photon transport—induced by multiple reflection from the higher-albedo surface areas—prevailed under overcast skies. However, a wide variety of natural variability introduced much greater variability in the measured irradiances as compared with the idealized MC predictions. Sources of variability included broken scattering layers beneath the main stratiform cloud layer (“scud”) and greater spatial complexity in the actual surface albedo distribution than was practical to simulate with the MC model. Considering all the sources of variability in the real Arctic troposphere, it is possible to conceive of a very large number of MC simulations. It is probably not worthwhile to perform such a large set of simulations until there are UAV data to interpret. Instead, we provide here a basic set of idealized MC simulations to demonstrate 3D radiative transfer effects that might be expected to prevail much of the time. Forthcoming UAV experiments can reveal whether these predicted effects are realistic and then suggest more detailed radiative transfer studies.

Figure 1 shows a photomosaic obtained during the Surface Heat Budget of the Arctic Ocean (SHEBA) campaign (Uttal et al. 2002). These digital images were acquired from a helicopter on 25 July 1998 at an altitude of 1.8 km. For this study a subset of this mosaic has been classified into ice, melt pond, and open water locations using a watershed segmentation algorithm available with the Python scikit-image software library. Similar to Podgorny and Lubin (1998), we first consider idealized heterogeneous surface conditions and then we simulate how the upwelling radiation field would be measured above realistic summertime Arctic sea ice cover as depicted in Fig. 1.

Fig. 1.
Fig. 1.

(left) SHEBA mosaic (original) image 4653 × 5687 pixels with a pixel size of 2.0 m, (top right) subset of the original image 500 × 500 pixels, and (bottom right) segmented subset of the original image. Red dots on the original image show locations of the subset image, and red dots on the subset images show the area used for the simulations that follow. Open water areas are shown in blue, and melt ponds are depicted in turquoise.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

2. Monte Carlo model

We use a backward MC model to simulate the 550-nm irradiance and hemispheric albedo a UAV radiometer system would measure at various flight altitudes below an optically thick cloud with a base altitude of 1 km above a horizontally inhomogeneous surface. The radiative transfer model is a monochromatic backward version of the 3D broadband Monte Carlo Aerosol Cloud Radiation model (MACR) developed at the Center for Clouds, Chemistry and Climate (C4), Scripps Institution of Oceanography from 1996 to 2005 [see Chung et al. (2005) and references therein for details about model architecture, model validation, and variance reduction techniques]. Under the backward MC approach, a photon is started at a given UAV altitude and then it is made to undergo multiple scattering in the atmosphere and clouds and multiple collisions with the reflecting surface. The photon is assigned a statistical weight that is adjusted in order to account for the probability of absorption and is also used to find the flux contribution from the sun at each scattering interaction and reflection from the surface. We run two separate simulations for the upwelling and downwelling irradiances.

For this study, the MACR code has been adapted for the Arctic to trace photons in the atmosphere and clouds using the maximum cross-sectional method, and to simulate Rayleigh and Henyey–Greenstein scattering and Fresnel and Lambertian reflection from the inhomogeneous surface. Python scikit-image and NumPy packages are used to convert JPEG (or other image formats) to 2D arrays of surface types (open water, open melt ponds, and snow-covered ice) for use as input data. Cyclic horizontal boundary conditions are employed for 2D surface albedo distributions. We make the approximation of a smooth ocean surface; the albedo of a water surface is typically an order of magnitude smaller than that of the ponded or snow-covered ice cover, and in this study we are primarily interested in the radiative effect of the stepwise discontinuity between the adjacent surface types.

Since the main focus of this study is the effect of the surface optical inhomogeneity on radiative transfer in a cloudy atmosphere, we adopt a simplified description of the clouds, approximating them as a plane-parallel layer whose optical properties remain constant in both the horizontal and vertical directions similar to Podgorny and Lubin (1998). The Arctic clouds considered in this study are taken to be mainly liquid water stratiform clouds typical for summertime, so Mie scattering or a suitable approximation thereof may be used instead of more complicated phase functions of ice crystals. Here we use the Henyey–Greenstein phase function, which is a widely accepted approximation for shortwave cloud scattering in primarily diffuse radiation conditions (e.g., Briegleb 1992). We note that this phase function would not be appropriate for simulating reflected radiances from a cloud top, particularly over mixed-phase clouds. The cloud is horizontally homogeneous with optical depth τc = 9, which is typical for the high Arctic in July (Dong and Mace 2003).

The model atmosphere spans altitudes from the surface up to 100 km and has 33 reference levels. Below 25 km each layer is 1 km thick. The vertical temperature and pressure profiles are those from the U.S. Air Force Geophysics Laboratory (AFGL) standard subarctic summer atmosphere. Rayleigh scattering and ozone absorption coefficients are tabulated on the reference levels and then are linearly interpolated between the reference levels in the process of the MC computation.

3. Results

We first examine how the radiation field varies along the cross section of a sea ice lead of varying width (Fig. 2). At a flight altitude over a narrow lead (200 m), the measurable albedo is reduced by only 15%–20% along a transect length of nearly 1 km. For the narrower leads, the measured albedo drops moderately (by ~0.2) at altitudes higher than 400 m, over a transect length approximately 3 times the width of the lead. For the wider leads, the decrease in measured albedo is greater, but above 300 m the measured albedo is never as low as that of the open water segment itself. This spatial variability results from multiple reflection of photons between the ice and the cloud base that enhance the upwelling and downwelling irradiance over the open water within the lead. Figure 3 shows this horizontal smoothing of the downwelling radiation for the wider leads. For the narrower leads, the downwelling is nearly entirely uniform in the horizontal and the presence of the lead can be discerned only in the upwelling irradiance (figure not shown).

Fig. 2.
Fig. 2.

Simulated albedo as measured from the UAV flying across leads (a) 200, (b) 400, (c) 800, and (d) 1600 m. Areas of low reflectance: open water with Fresnel reflection; areas of high reflectance: sea ice with an albedo of 0.75.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

Fig. 3.
Fig. 3.

Downwelling irradiance over the idealized sea ice leads of Fig. 2, having width (left) 800 and (right) 1600 m. Irradiance is relative to F0cosθ0 = 1.0 at the top of the atmosphere, where F0 is the extraterrestrial solar irradiance at 550 nm and θ0 is the solar zenith angle.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

These effects are elucidated further in Fig. 4, which shows the radiation components averaged over the 3000-m-wide transect of Fig. 2, as a function of altitude. Because of multiple reflection of photons from the cloud base, downwelling irradiance is generally large and uniform with altitude for all sea ice lead widths. There is much more variability for the upwelling irradiance. The upwelling irradiance over the 200-m lead is twice as large near the surface as over the 1600-m lead, an obvious result of a smaller open water area, but we also see a greater increase with altitude for the narrower versus wider leads. The altitude and lead width dependence in the albedo essentially follows that of the upwelling irradiance. Net fluxes near the surface are larger for wider leads, while at altitude the net flux decreases as the horizontal photon transport increases the effect of the highly reflective ice surface.

Fig. 4.
Fig. 4.

(top left) Upwelling irradiance, (top right) downwelling irradiance, (bottom left) albedo, and (bottom right) net flux averaged along a horizontal flight track from one side of Fig. 2’s cell to the other. Leads 200 m [red; (a) in Fig. 2], 400 m [blue; (b) in Fig. 2], 800 m [green; (c) in Fig. 2], and 1600 m [gray; (d) in Fig. 2].

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

In Fig. 5 we consider the full two-dimensional behavior of the UAV-measurable albedo at four low flight altitudes. At 10 m above the surface, the open water and melt pond features are distinguishable, but by 20 m altitude the melt pond influence becomes indistinct. By 50 m altitude, the largest (~200-m dimension) open water feature still reduces the measurable albedo by a factor of 2 directly above it, but the smaller open water features have become much less distinct with albedo reductions of only ~0.15. At 100 m altitude, only the largest open water feature is distinct and it reduced the measurable albedo by 0.10–0.15 directly above it.

Fig. 5.
Fig. 5.

Simulated albedo as measured from the UAV flying above the image subset shown in Fig. 1 at altitudes (a) 10, (b) 20, (c) 50, and (d) 100 m. Areas of low reflectance: open water with Fresnel reflection; areas of high reflectance: sea ice with an albedo of 0.75. Note the scale change in the legend between the top and bottom panels.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

We emphasize that the results shown in Fig. 5, and also those of Figs. 2 and 3, cannot be obtained by a plane-parallel radiative transfer model using an independent pixel approximation. An array of 1D radiative transfer calculations, even with each having a distinct surface albedo, will not simulate the horizontal photon transport that is the major effect and the key result of this 3D study. The one exception is an independent pixel approximation specifically modified to include a correction for horizontal photon movement (e.g., Marshak et al. 1995), but even this usually requires an MC simulation to generate the required parameterization.

We now consider some sensitivity studies with more realistic atmospheric variability. Arctic stratiform clouds show pronounced horizontal inhomogeneity. For example, Lubin and Vogelmann (2011) retrieved downwelling optical depth from shortwave spectroradiometer measurements at 1-min intervals under clouds that appeared highly uniform to the unaided eye. In one representative example, the sample mean optical depth was 7.7 with a standard deviation of 4.4. Arctic aerosol is often well mixed in the lower troposphere (e.g., Bates et al. 2013), and here we adopt an aerosol with an optical depth of 0.2 between 0 and 1000 m, with a 550-nm single-scattering albedo of 0.887 and an asymmetry factor of 0.721 (Hess et al. 1998). Figure 6 shows the radiative components above a point exactly in the center of the 500 × 500 pixel subset image of Fig. 1. Under the range of cloud optical depths considered (τc = 7.7 ± 4.4), the radiation underneath the cloud (base: 1000 m) is almost entirely diffuse, and despite variability in the downwelling and upwelling irradiances, the albedo is essentially invariant to cloud optical depth. However, the downwelling irradiance profile with aerosol shows a decrease as we approach the surface, as a result of the absorption in addition to scattering. This yields lower albedos and net fluxes at altitudes above 200 m, compared with cases of cloud plus Rayleigh scattering. We also considered a solar zenith angle of 75° in addition to 60°. In the diffuse radiation environment under the cloud, there is little noticeable effect on the albedo as the upwelling and downwelling irradiances scale proportionally (figure not shown). In Fig. 7 we consider the effect of an anisotropic sea ice surface for the same location as in Fig. 6. We adopt the empirical bidirectional reflectance distribution function (BRDF) of Lindsay and Rothrock (1994) and implement it in the MC model using rejection sampling (e.g., Martino and Míguez (2011). Because radiation below the cloud incident on the surface is nearly entirely diffuse, the inclusion of a BRDF has little effect on the vertical radiation profiles. However, the impact of the aerosol layer is just as pronounced as before, compared with the cases of cloud plus Rayleigh scattering. In Fig. 8 we consider a different location, exactly 100 pixels to the left of center in the subset of Fig. 1. Here, we are over a triangular section of open water. The lower surface albedo dominates the radiation field, and we do not see the local maximum in upwelling irradiance and albedo that we notice over the melt pond.

Fig. 6.
Fig. 6.

As in Fig. 4, but for above a point exactly in the middle of the 500 × 500 pixel subset of Fig. 1, above a melt pond, for varying τc: 3.3 (gray), 7.7 (blue), 9.0 (green), 12.1 (black), and 9.0 with aerosol (red); θ0 = 60°.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

Fig. 7.
Fig. 7.

As in Fig. 6, but for τc = 9.0 and Lambertian surface (black), BRDF for sea ice surface (blue), and Lambertian surface with aerosol (red); θ0 = 60°.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

Fig. 8.
Fig. 8.

As in Fig. 6, but for above a point exactly 100 pixels to the left of the central point considered in Fig. 7, above a triangular section of open water.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

Finally, in Fig. 9 we consider a shorter wavelength of 380 nm. Cloud scattering is essentially unchanged, but Rayleigh scattering is stronger as is aerosol absorption. We scaled the aerosol optical depth from 0.2 at 550 nm to 0.348 at 380 nm using an Angström exponent α = 1.5 (Tomasi et al. 2015). Following Blanchet and List (1983) for Arctic aerosol, we scaled the 380-nm single scattering albedo and asymmetry factor to 0.90 and 0.730, respectively. The radiation components show the impact of this enhanced aerosol extinction at 380 nm relative to 500 nm.

Fig. 9.
Fig. 9.

As in Fig. 8, but for τc = 9.0, Lambertian surface, and aerosol uniformly distributed below cloud, for wavelengths 550 (green) and 380 nm (violet); θ0 = 60°.

Citation: Journal of Atmospheric and Oceanic Technology 35, 1; 10.1175/JTECH-D-17-0066.1

4. Discussion

Stratiform cloud cover is the prevailing sky condition over the Arctic Ocean during the periods of sea ice transition (Intrieri et al. 2002; Smith et al. 2017), and it strongly regulates the shortwave and longwave fluxes incident on the sea ice–ocean system (Lubin and Simpson 1997; Dong and Mace 2003). In addition, this study shows how horizontal photon transport by multiple reflection between a cloud base and a high-albedo surface influences how albedo and surface energy fluxes would be measured by a UAV. If one is interested in sampling the local contrasts between specific surface types, then the UAV must fly at a low altitude (<20 m); at altitudes higher than 100 m, the airborne radiometers will sample irradiances that are greatly smoothed horizontally due to photon multiple reflection. MC simulations similar to this preliminary study can help design sampling strategies for Arctic surface energy budget studies. For example, one might first fly a grid at low altitude to detect contributions from individual surface features, followed by a similar or more loosely spaced pattern at higher altitude to directly measure how irradiances influenced by the individual surface features blend to produce an average over an area of interest, such as a satellite remote sensing footprint or a high-resolution regional model grid cell.

One limitation of this study is that it considers a static radiation field that may not be representative of what is measured by a moving aircraft. Small fixed-wing research UAVs have cruise speeds of ~25 m s−1 (e.g., Bates et al. 2013). The response time of UAV-adapted radiometers varies from 100 ms (e.g., de Boer et al. 2016) to 1 s (e.g., Reineman et al. 2013). At the faster response times, the measured spatial albedo variability might be expected to follow the overall conclusions of this study, while the slower response times may cause some smearing of the spatial variability. Presumably one would prefer to fly a fixed-wing aircraft primarily on horizontal transects for radiometric measurements rather than orbiting about a single location (in banked flight); hence, instrument response time and sampling rate must be factored into experiment design. Overall, this study demonstrates the importance of horizontal variability in surface albedo and the noticeable influence of aerosol extinction, with less influence from horizontal cloud optical depth variability, for UAV-measured radiation components below an Arctic cloud deck. It will be interesting to compare these idealized cases with forthcoming Arctic UAV data.

Acknowledgments

This study was supported by the U.S. Department of Energy under Award DE-SC0008502.

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