**4. Discussion**

#### *4.1. Northern Hemisphere Albedo from VSIA*

VSIA albedo offers a fine-resolution, large-scale albedo data source. Figure 14 shows monthly albedo maps in 2014 for the Arctic region as a sample of the algorithm performance. The dynamic evolution of albedo over time is mainly caused by the melt timing and intensity. The coverage of the retrieved albedo increases from January to April after the winter solstice. Then albedo stays at a high value because of the covered, cold, optically thick snow. As temperature increases from May to August, the snow begins to melt, thereby decreasing the surface albedo. Due to the formation of larger melt ponds, the albedo value decreases rapidly during this period. Once the new seasonal ice begins to freeze from ponds and open water, albedo increases again. From October, the data in the central Arctic is missing during the polar night period.

**Figure 14.** VSIA over 50◦~90◦N on the middle day of each month in 2014. The gray-colored region, including the polar night, has no data due to SZA cut-off of the LUT. The land and sea water background adopt the Cross Blended Hypso with Shaded Relief and water [50].

#### *4.2. Analysis of VSIA LUT*

The VSIA LUT provides mathematical weights used to convert TOA reflectance to surface broadband albedo, reflecting the energy contribution among different bands at each specific angular bin. Due to the numerical regression process, the coefficients' magnitudes have lost their direct link to the BRDF directional reflectance intensity, but still reflect some directional variation patterns. For sea-ice covered regions, the SZA is normally larger than 40◦, so we picked 60◦ as an instance to observe the hemispherical variation trend of the coefficients at each SDR band. Figure 15 demonstrates

the polar plots of the band coefficients at various VZAs and RAAs with constant SZA. Generally, the polar plots demonstrate the continuity and rationality of VSIA LUT at angular dimensions.

The most apparent feature of all plots is the bright/dark spot in the forward scattering direction, which is formed due to specular reflection over the snow/ice/seawater surface. The specular component in BRDF is in accordance with geometric optics. Its contribution varies with the sea-ice surface physical characteristics and the solar zenith angle. It is shown that the center points of these spots are all around the symmetry point of solar incident direction. The size of the specular reflection spot varies among different bands due to the angular distribution of the spectral reflected flux. For instance, the center wavelengths of M02 and M03 are close, thus their coefficients show similar hemispherical variation patterns.

The phenomenon that the albedo uncertainty increases at larger SZAs shown in Section 3.2.4 is partly due to the increasing spread of LUT coefficients. Here we calculated the coefficient of variation of LUT coefficients at consecutive SZA intervals, as shown in Figure 16. The coefficient of variation measures the relative variability, which is the ratio of the standard deviation to the mean value. The samples cover the whole VZA range. To eliminate the influence of the specular reflectance spot regions, the RAA was divided into two ranges, 0◦~150◦ and 150◦~180◦, shown separately in Figure 16. The left figure contains a larger portion of RAA values and represents the majority of observations. It shows that the spread of coefficients in the SZA range of 70◦~79◦ is more significant than other ranges at most visible bands. This causes the larger spread of LUT coefficients at larger SZA values. In the forward scattering cases shown in the right figure, the SZA range of 50◦~69◦ corresponds to larger coefficients of variation. But its influence is limited due to the smaller RAA range. The magnitude of bar plots at different bands is related to the spectral sensitivity of albedo to SDR reflectance. The highest value is shown at M05 with a center wavelength of 0.672 μm (light red).

**Figure 15.** *Cont.*

*Remote Sens.* **2018**, *10*, 1826

**Figure 15.** *Cont.*

**Figure 15.** The polar plots (using a polarBRDF tool developed by Singh [51]) shows the coefficients corresponding to the horizon-to-nadir coverage. The bands and central wavelengths are: (**a**) the constant term; (**b**) M01 (0.412 μm); (**c**) M02 (0.445 μm); (**d**) M03 (0.488 μm); (**e**) M04 (0.555 μm); (**f**) M05 (0.672 μm); (**g**) M07 (0.865 μm); (**h**) M08 (1.24 μm); (**i**) M10 (1.61 μm); (**j**) M11 (2.25 μm). Relative azimuth angle represents the angle between lines joining the point and the center of the polar plot. An azimuth of 0◦ (360◦) represents backward scattering while 180◦ indicates forward scattering. The actual relative azimuth angle (RAA) range of VSIA LUT is [0◦~180◦]. The 180◦~360◦ hemispherical image mirrored the 0◦~180◦ hemispherical image for illustration integrity.

**Figure 16.** The variation of LUT coefficients at adjacent SZA ranges of each band (corresponding to one specific color). (**a**) The coefficient samples cover all view zenith angle (VZA) ranges and the RAA range of 0◦~150◦; (**b**) the samples cover all VZA ranges and the RAA range of 150◦~180◦.

#### *4.3. Limitations in Current Algorithm and Validation*

Currently, sea-ice albedo data is going to be produced in the VIIRS albedo environmental data record (EDR). Reliable albedo values were reported through the validation and test in the algorithm readiness review; however, the current VIIRS albedo product over the sea-ice surface still suffers from several issues:

#### 1. Limited validation data on the sea-ice surface

Admittedly, the power of this study is inevitably restricted by the limited sea-ice surface measurements due to rare physical access. The albedo of glacier and sea ice is influenced by the same factors [52], and most of the sea-ice components or their proxies, the ice, snow, and pond, can be found around the Greenland AWS sites, except the sea water surface, which has a very low and relatively constant albedo. Therefore, the long-term monitoring data from the AWS on Greenland has provided substitute reference data for a variety of sea-ice surface conditions, such as the optically thick sea ice with snow cover or melt ponds. It can be seen that the albedo evolution trend over the PROMICE stations, as referred to in the time-series plots in Figure 6, is consistent with the multi-year Arctic sea ice [53].

For seasonal young sea ice, its albedo is typically less than the multiyear sea ice during the melting season and pond evolution [54]. Considering the lack of representativeness of Greenland AWS measured albedo to seasonal sea ice, we also cited some sea-ice albedo measurements as complementary data, which cover the surface conditions such as young sea ice and thin melt ponds. Considering the sample number of the in situ sea ice measurements is limited, further validation attempts are expected to understand the product accuracy, such as cross-comparison with other sea-ice albedo products.

#### 2. Significant validation uncertainty at large SZA

Large SZA affects the accuracy of both VSIA and PROMICE measurements. AWS sensors suffer from the intrinsic cosine response error at large solar zenith angles, which is reported to reach a maximum of 8% at a solar zenith angle of 80◦ [55]. Even for solar zenith angles less than 75◦, we should expect a cosine response error around 5% [56], which can even be amplified by the riming. For VSIA, the ART model for snow/ice BRDF simulation is applicable at high solar zenith angles up to 75◦ [57,58].

3. Thorough spatial representative investigation is desired

In this study, we did not exclude any match-ups influenced by strong ground heterogeneity since high product performance under all conditions is expected. However, it has been investigated that ground heterogeneity around the sites will amplify the uncertainty in validation at different spatial scales [59]. In this way, further investigation using higher resolution imageries as ancillary data is on schedule.

4. Further investigation on the overestimation reason

The evaluation result shows an overestimation of the VSIA albedo. However, several issues should be kept in mind before drawing this conclusion. First, the ground measurement data does not represent the "true" value considering the big scale gap between the ground point measurement and the satellite pixel retrieval. Second, the measurements from the flux instruments contain certain uncertainty [55], due to the tilting/leveling errors and the cosine-response error of the instruments. Third, the seawater component is absent in this evaluation. According to the current result, the VSIA product performs very well in the low albedo condition; however, the missing seawater component might take some unknown influence into the algorithm performance. To solve this problem, we plan an inter-comparison by introducing other coarser resolution satellite sea-ice albedo products.

5. Influence of sea-ice algae has not been considered

Algae aggregates alter the optical properties including albedo of pond areas [60,61]. The short-lived algal layer growing on the bottom of the ice in springtime resulted in an increasing of the radiance absorption and possible decreasing of surface albedo. This influence was not considered in the theory used for pond simulation in our algorithm, which could be one reason for the overestimation of the VSIA. The improvement of the model to represent the algae optical properties is expected.

#### 6. Some assumptions of the ART model may be violated in the Arctic

The ART model performs well in reproducing the snow/ice reflectance, but still suffers from many problems. First, it is valid for weakly absorbing semi-infinite turbid media [57] so that its validity over the first-year ice still needs further evaluation, since the sample used here is small. Second, the model assumes a flat smooth surface condition. This simplification increases the retrieval uncertainty due to slope and surface roughness [47].

The sea-ice surface roughness also affects the albedo significantly. Increased roughness generally alters the incident and reflected radiation. Its influence on the albedo thus depends on the ratio of diffuse to total incoming radiation. The evaluation of such an effect deserves more extensive work, i.e., considering micro-tomography adjustment in the regression.
