Evaluation of the MODIS (C6) Daily Albedo Products for Livingston Island, Antarctic

: Although extensive research of Moderate Resolution Imaging Spectroradiometer (MODIS) albedo data is available on the Greenland Ice Sheet, there is a lack of studies evaluating MODIS albedo products over Antarctica. In this paper, MOD10A1, MYD10A1, and MCD43 (C6) daily albedo products were compared with the in situ albedo data on Livingston Island, South Shetland Islands (SSI), Antarctica, from 2006 to 2015, for both all-sky and clear-sky conditions, and for the entire study period and only the southern summer months. This is the ﬁrst evaluation in which MYD10A1 and MCD43 are also included, which can be used to improve the accuracy of the snow BRDF/albedo modeling. The best correlation was obtained with MOD10A1 in clear-sky conditions (r = 0.7 and RMSE = 0.042). With MCD43, only data from the backup algorithm could be used, so the correlations obtained were lower (r = 0.6). However, it was found that there was no signiﬁcant difference between the values obtained for all-sky and for clear-sky data. In addition, the MODIS products were found to describe the in situ data trend, with increasing albedo values in the range between 0.04 decade − 1 and 0.16 decade − 1 . We conclude that MODIS daily albedo products can be applied to study the albedo in the study area. Author Contributions: Conceptualization, A.C.-P. and J.F.C.; methodology, A.C.-P.; software, A.C.-P.; validation, A.C.-P., J.F.C. and S.F.; formal analysis, A.C.-P., J.F.C. and C.R.; investigation, A.C.-P. and J.F.C.; data curation, A.C.-P.; writing—original draft preparation, A.C.-P.; writing—review and editing, A.C.-P., J.F.C. and C.R.; supervision, J.F.C. and C.R.; project administration, J.F.C. and C.R.; funding C.R.


Introduction
Albedo or bi-hemispherical reflectance is the ratio of the radiant flux reflected from a unit surface area into the whole hemisphere to the incident radiant flux of hemispherical angular extent [1]. The albedo analysis is of interest both to climatology in general [2] and to the climatology of polar areas in particular. Snow cover has a significant impact on the hydrological cycle during winter and spring on the Earth's surface [3], mainly in the polar areas, where melting of the permafrost would lead to an increase in temperature due to the release of greenhouse gases [4]. However, the greater or lesser degree of surface melting is not only due to changes in temperature; an albedo increase would cause the snow to absorb a smaller amount of short-wave radiation, which would lead to a reduction in the energy available for melting [5]. It is known that variations in albedo are strongly related to the surface energy balance and the available melting energy [6][7][8][9]. Thus, albedo analysis in the polar areas is essential for the study of climate change.
Satellite observations are currently essential for observing the evolution of the albedo in polar areas, mainly in Antarctica, where, due to adverse weather conditions, the weather station network is not able to cover the entire territory. Thus, for example, Laine [10] used satellite data to analyze the albedo behavior in five sectors around Antarctica (the Weddell Sea, the Indian Ocean, the Pacific Ocean, the Ross Sea, and the Bellingshausen-Amundsen Sea) between 1981 and 2000, finding an increasing albedo trend during spring and summer DHR = 2π 0 π/2 0 f r (θ i , ∅ i ; θ r , ∅ r ) cos θ r sin θ r dθ r d∅ r , (1) where DHR is the directional hemispherical reflectance, f r (θ i , ∅ i ; θ r , ∅ r ) is the BRDF (Bidirectional Reflectance Distribution Function), θ i and ∅ i are the angles defining the incident radiation direction, and θ r and ∅ r give the direction of the reflected radiation. The MCD43 product provides, in addition to the black-sky albedo, the white-sky albedo [27]. The whitesky albedo is the bi-hemispherical reflectance (BHR) for pure diffuse isotropic radiation and is defined by Schaepman-Strub et al. [1] as: where BHR is the bi-hemispherical reflectance for pure diffuse isotropic radiation and ρ is the reflectance. Therefore, when comparing in situ albedo with MODIS daily albedo products, it should be noted that the albedo provided by the pyranometers at the ground stations is the BHR. If the incident radiation is divided into direct and diffuse parts, and the diffuse part is assumed to be isotropic: where ρ dir is the DHR (black-sky albedo), d is the fractional amount of direct irradiance, and ρ di f f is the BHR for pure diffuse isotropic radiation (white-sky albedo). For this reason, in this article, the albedo was analyzed for both all-sky conditions and clear-sky conditions. In situ albedo is blue-sky albedo and, as such, it should be compared with MODIS bluesky albedo. The calculation of the MODIS blue-sky albedo requires the calculation of d in Equation (3). According to Equation (3), in the special case that the direct albedo is equal to the diffuse albedo, we have BHR = ρ dir = ρ di f f . The relationship between ρ dir and ρ di f f has been studied for several surface types [28,29]. In general, the discrepancy between ρ dir and ρ di f f increases with increasing solar zenith angle (SZA), due to the significant dependence of ρ dir on the SZA, whereas ρ di f f does not change with SZA. However, in the case of snow, the direct albedo is taken to be equal to the diffuse albedo for SZA < 60 • [30], whereas for SZA > 60 • the direct albedo is taken as Briegleb [29], and Wang and Zeng [30]: In the case of the study area, SZA < 60 • at local noon from September 30 until March 12 each year, which represents 74% of the total number of days considered in the study. This means that, for data between September 30 and March 12, we can take BHR = ρ dir = ρ di f f , i.e., WSA and BSA MODIS data can be compared to in situ data directly. From this range of dates, we can evaluate the difference between ρ dir and ρ di f f as: The value of e increases almost linearly with increasing SZA. The maximum value of e (e max ) occurs for September 1 (SZA = 70.74 • at local noon) and for April 10 (SZA = 70.84 • at local noon). Taking typical values of snow for the diffuse albedo, we can calculate the corresponding ρ dir using Equations (4) and the relative difference from Equation (5); we obtain e max = 0.06 (6%) for ρ di f f = 0.7 and e max = 0.035 (3.5%) for ρ di f f = 0.8. We consider that a direct comparison of in situ data with WSA and BSA separately is appropriate. This assumption is reinforced by the fact that BSA and WSA attain very similar values in the dates considered in the study. The calculation of MODIS blue-sky albedo, in the case of snow, would be relevant for SZA values above those considered in this work, or in cases in which MODIS albedo data is used in models requiring high-precision albedo values.
Several investigations have been carried out on the comparison between the results of the last two versions (collections) of the cited MODIS products: the previous collection 5 (C5) and the currently available collection 6 (C6), e.g., [31][32][33][34]. C6 of MOD10A1/MYD10A1 shows important changes compared to C5, including the replacement of the Fractional Snow Cover (no longer calculated) by the Normalized Difference Snow Index (NDSI) Snow Cover. In addition, snow detection errors have been reduced, and a new quality control bit flag has been implemented [35]. In the case of MCD43A3, its C5 provides images each 8 days over a composite period of 16 days [31]. In contrast, its C6 provides daily data, although it also uses the 16 day data, which are temporally weighted to the ninth day of the 16 day [13]. The improvements described above for the MODIS albedo products and, in general, the fact that C6 corrects the drift shown by the C5 data [32,34], makes it necessary to update the studies that were carried out C5, as suggested by Casey et al. [32], especially in the polar areas. Therefore, the aim of this work is to evaluate the albedo behavior on Livingston Island, Antarctica, based on data from MODIS C6 albedo products and to compare it with in situ albedo behavior, both for all-sky and clear-sky conditions. In addition, the results obtained from the MOD10A1 C6 albedo in this work were compared to those of the MOD10A1 C5 albedo, summarized in a previous study conducted by Calleja [12].
Following Section 1 (Introduction), in Section 2 (Materials and Methods) we describe the study area, the data used, and the methodology used to compare the MODIS albedo products with the in situ data. The results and discussion are provided in Section 3, and Section 4 presents the conclusions.

Study Area
The study area comprises Livingston Island, the second largest island in SSI, in the maritime Antarctica ( Figure 1). Although in this island is the Byers Peninsula, the largest ice-free area in the archipelago [36], 90% of the island is covered by glaciers [37]. It is known that the decrease in albedo in the polar zones would have important consequences for the global energy balance on the Earth's surface. For this reason, the use of satellite data with high temporal resolution is essential to obtain a systematic monitoring of the albedo in these areas, where it is difficult to obtain in situ data. However, there are still insufficient evaluations for Antarctica of MODIS products, which have been extensively evaluated in the Greenland ice sheet. In addition, the distribution of permafrost is complex in the South Shetland Islands [38]. It is therefore an area of special interest for the monitoring of climatological variables in the maritime Antarctic. Our study focuses on the Hurd Peninsula, where two ground stations of the Spanish Meteorological Agency (AEMET) are located (Table 1) (Table 1). As can be seen in Figure 1 and Table 1, the study area is near 60 • S, considered the cloudiest place in the southern hemisphere, with around 85-90% cloud cover throughout the year [39]. In the SSI archipelago, the persistence of cloudiness is related to the dynamic circulation of air masses and atmospheric fronts [40]. The in situ albedo data used in this work were obtained from the JG station, which provides albedo data every 10 minutes. Albedo was measured at JG using two Kipp-Zonen CNR-1 pyranometers, one for incident radiation (global and direct) and another for reflected radiation. The pyranometers are placed 3 m above the snow and they are replaced each two years with calibrated ones [12]. Direct and diffuse radiation were obtained from the JCI station, which provides values of diffuse radiation (measured with KIPP-ZONEN CM11 pyranometers) and direct radiation (measured with KIPP-ZONEN CH1 pyranometers) each ten minutes To determine the cloudiness in the area and thus confirm whether MODIS errors in cloud detection affect albedo estimation, direct and diffuse radiation measurements are necessary. Knowing both radiations, the clearness index (clr) was calculated using JCI data as representative of the study area, as advised by specialists from the Antarctic AEMET stations [41].

MODIS Data
As stated in the introduction, the daily MODIS albedo products are MOD10A1, MYD10A1, and MCD43, all of which have a spatial resolution of 500 m. The data for these products were downloaded from the Google Earth Engine platform (http://earthengine. google.org) [42].
The snow albedo products, MOD10A1 (Terra) and MYD10A1 (Aqua), provide albedo values from the best daily observation [35]. C6 of both products consists of seven layers: NDSI_Snow_Cover, NDSI_Snow_Cover_Basic_QA, NDSI_Snow_Cover_Algorithm_Flags_QA, NDSI, Snow_Albedo_Daily_Tile, orbit_pnt, and granule_pnt. It is also important to note that, in C6, the Aqua band 6 data, defective in C5, has been restored and, therefore, constitutes scientifically valid data for the snow algorithm. Thus, the same algorithm is used for Terra and Aqua [35]. The MCD43A3 product provides black sky albedo (BSA), i.e., DHR, and white sky albedo (WSA), i.e., BHR, data for the MODIS bands 1 to 7, the visible (VIS), near infrared (NIR), and shortwave infrared (SWIR) bands [13]. MCD43A1 provides three model weighting parameters for MODIS spectral bands 1 through 7 [43]. MCD43A2 contains BRDF/Albedo band quality and days of valid observation within the 16 day period for MODIS bands 1 through 7 [44].
MOD09GA/MYD09GA (Terra/Aqua) C6 were used to check, by visual inspection, whether the day was classified as cloudy or clear, when in situ and MODIS albedo data were available but no direct/diffuse radiation data were available in JCI, which meant that the clr index could not be calculated. Visual inspection was used to detect cloud mask failures in MODIS products [41]. These products, also at a spatial resolution of 500 m, provide the atmospherically corrected surface spectral reflectance in bands 1-7 [45,46]. The RGB: 1-6-7 composition was used for the visualization, for which the central wavelength of these bands was 645, 1640, and 2130 nm, respectively. This composition is useful because it distinguishes the cloud pixels (in white) from the snow pixels (in red) [12,47].

Albedo Filtering
In the case of the in situ data, the daily albedo was obtained as the mean of the measurements satisfying the condition that the solar zenith angle (SZA) < 75 • , using similar criteria to those of Stroeve et al. [48] and Wang and Zender [49]. In addition, it is known that at higher angles there are biases in the results [25,50]. Therefore, we excluded the data from May, June, July, and August from the study, because in these months SZA > 75 • .
Pirazzini [51] also showed that SZA has a different impact on albedo, depending on the size of the grain and the type of snow (fresh or aged); and Yamanouchi [52] found that it has a strong dependence on eroded snow. In addition, Konzelmann [53] described that the maximum fresh snow albedo for clear-sky conditions is 0.84. Thus, albedo values greater than 0.84 were eliminated.
For the satellite data, in regards to MOD10A1 and MYD10A1, only the highest quality data (QA = 0) were used. Once this filter was applied, no data were obtained with SZA > 75 • . MCD43, as explained in the previous section, did not have good quality data in the study area, so the SZA filter was applied, removing the data with SZA > 75 • . Considering the albedo upper threshold, there is evidence of a positive bias in MODIS data above 0.84 [20]. The improved albedo products in MODIS C6 decreased the data variability and eliminated very low, clearly erroneous, values obtained in C5. However, very high values were found; thus, to follow the same criteria applied to the in situ data, albedo values higher than 0.84 in the C6 products were discarded in this work.
Furthermore, because snow metamorphism proceeds slowly in cold places such as Antarctica, we consider that there should be no sharp increases or decreases in the albedo, with the exception of snowfall episodes or windstorms [54]. Therefore, a moving average with a 3 day window was calculated, taking into account three consecutive dates of data (not necessarily three consecutive calendar dates), for all data after applying the SZA filter and eliminating values greater than 0.84. A small window was selected because it allows changes to be captured that could occur due to sudden snowfalls. Dates with unusually high absolute values of residues were analyzed (≥ |0.15|) and the Square Mahalanobis Distance (SMD) was calculated as: where x is the vector of albedo data, µ is mean vector, S is the covariance matrix, and (x − µ) is the transpose of the vector. SMD accounts for the covariance of data, and indicates the distance from a point to a distribution in multidimensional space; its associated p-value was used to rule out outliers [55,56]. SMD, which allows anomaly detection, has been successfully used to process remote sensing time series, e.g., specifically MODIS [57] and image processing [58]. The SMD threshold was selected with three aspects in mind: first, to retain as much of the dataset as possible; second, to ensure that outliers did not introduce bias into the data analysis; and, finally, to set the same threshold for all MODIS products. Therefore, the mean of SMD standard deviation (s) of all MODIS albedo products was calculated and values exceeding 1.5 s (SMD > 4) and whose associated p-value ≤ 0.05 were considered outliers and rejected. The statistical test s was applied to establish thresholds for data selection in remote sensing [20,32,59,60].

Clearness Index (clr)
The clearness (or cloud) index was calculated from Equation (7), following to Wang and Zender [49], who obtained it from a simplified test of normalized fuzzy ratio variability of clear sky [61]: where clr is the clearness index, which varies in a range from 0 (cloudy sky) to 1 (clear sky), although normally its values are below 0.95 due to the influence of atmospheric aerosols. Days with clr < 0.3 are defined as overcast. DIR is direct radiation and DIF is diffuse radiation. The daily mean clr was calculated using only those data with SZA < 75 • for the reasons mentioned in Section 2.3.1, to ensure that the clr value was not affected by measurements that did not satisfy the criteria selected for this work. The value of this index for cloudy days and clear days was then used to analyze the MOD10A1, MYD10A1, and MCD43 product data. When there was no radiation data but MODIS data were available, a visual inspection was performed to determine if the day was clear. This information improved data availability, which is often a problem in the area of study. Thus, it is important to incorporate as many data as possible to assess the correlation of MODIS albedo products with in situ data in our area.

MCD43 Data Processing
In the study area, only backup algorithm retrievals were obtained, due to the abundant cloudiness. This algorithm is based on a land cover classification and high quality data from MODIS full inversion BRDF retrievals from a previous year to estimate the surface BRDF. Although the values obtained by the backup algorithm are classified as low quality, they are sometimes as good as those obtained at the dates when the full inversion occurs [25,50,62,63]. Where full recovery cannot be obtained due to insufficient or poor sampling or inadequate adjustment, a backup method using available observations is applied [64]. Following these criteria, the backup algorithm was not excluded.
To be able to obtain albedo data comparable with that of other MODIS products and with in situ data, it was necessary to carry out the narrow to broadband conversion. First, all data were processed. Although Liang [65] presented an algorithm for the conversion of narrow to broadband albedo and showed that it could be applied to a large part of the land cover, in this work, Equation (8) proposed by Stroeve et al. [50] was used because it was designed specifically for snow cover: where α is the shortwave broadband albedo and b is the MODIS narrowband albedo for the specified MODIS spectral bands.

Albedo Trend
To calculate the albedo trend, locally weighted scatterplot smoothing (LOWESS) [66,67] was applied to the already filtered data of the months of January, February, and March of each year for all-sky conditions. It is calculated for the summer months in the southern hemisphere to avoid seasonal influences. This robust statistical method, which is usually applied to high-dispersion datasets, in addition to showing the trend in the long-term data, allows the effects of outliers to be minimized. LOWESS has multiple applications, including noise reduction in satellite-derived measurements [68]. The method is based on the adjustment of points from a polynomial regression in which the closest points have the greatest weight in the estimation of the regression. In this case, a value of 2/3 was assigned to the smoother span to prevent widely separated data from influencing each other. Using the LOWESS albedo values, albedo increases per day were obtained by linear regression, and then converted to values per decade.

Albedo Trend
This section shows the results of the albedo trend, analyzed with the austral summer data (J-F-M) during the whole study period. Only these months were selected to avoid biases caused by seasonal variations and also because data availability is highly variable in the remaining months. Although MODIS describes the temporal evolution of the in situ data, a greater dispersion in the satellite data was observed, as already referred to by, among other authors, Stroeve et al. [25] for Greenland and Calleja et al. [12] for our study area. It has been shown that the best results with MODIS are obtained after the application of filters that correct for the increase in temporal variability with respect to in situ data, described among others by Calleja et al. [12], Stroeve et al. [25], and Box et al. [20]. Figure 2 shows in situ albedo values, MOD10A1, MYD10A1, and MCD43 (BSA and WSA) for J-F-M. As can be seen, the distribution of the in situ data values is much more homogeneous than in the MODIS products, where extremely low values are observed. An increasing trend in albedo has been documented for the study area in the study period (2006-2015) based on data from MOD10A1 C5 and in situ data [12]. With C6 data, in all cases, there is an increasing trend. Table 2 shows the intercept of the albedo linear fit and the daily increment values (slope) for the in situ data (0.0000090), MOD10A1 (0.000035), MYD10A1 (0.000022), MCD43 BSA (0.0000428), and MCD43 WSA (0.0000420). The largest increases in MODIS are observed in the MCD43 products, both BSA and WSA, which represent an increase of 0.16 decade −1 and 0.15 decade −1 , respectively, whereas the MOD10A1 and MYD10A1 values are smaller (0.12 decade −1 and 0.09 decade −1 , respectively), although they continue to be above that of in situ data (0.04 decade −1 ). We also observed that the data source with the greatest dispersion with respect to in situ data is MCD43. This albedo increase could be related to several factors. In the Bellingshausen and Marsh stations of the SSI archipelago, a decreasing annual temperature trend has been described for the period 2006-2015 (−0.065 and −0.022 • C per year, respectively) [69]. This local cooling effect in the region was also documented by Plenzler et al. [70], who found in the vicinity of Arctowski Station a decrease in air temperature during summer 2013-2017. By comparison, a positive trend in the accumulation of snow and ice and an increase in the thickness of the snow cover at locations on Livingston Island have been described between 2008 and 2016 [71].
However, these arguments justify the increase in all data sources, but not the greater increase of MODIS with respect to the in situ data nor the greater dispersion observed in the first years of the study period. A dominant component of this error has been found to be the failure of MODIS to completely eliminate the effects of clouds, e.g., thin clouds and cloud edges [20]. These artefacts create abrupt variations in the surface albedo time series [59], and introduce both overestimation errors, partially eliminated here with the elimination of albedo values greater than 0.84, and underestimation errors. It should be taken into account that the study area pixel is covered by snow all year round, which would not justify very low albedo values. Furthermore, it has been documented that at latitudes poleward of 60 • S, the predominant cloud type is stratus [72], which is associated with the large number of depressions at this latitude [40]. Specifically, Angiel et al. [40] measured cloudiness using 0-8 octa cloud cover at the Arctowski station, in SSI for 2006, and they found that low-level stratocumulus and stratus clouds dominated the cloud cover structure. This could justify the low albedo values found, because stratus clouds have been associated with albedo values close to 0.5 [73], which is consistent with the albedo values . Therefore, we think that the presence of cloud cover could be one of the factors that increases the gap between in situ albedo and several MODIS albedo products. For example, if we analyze the total number of cloudy days in the months of January, February, and March used to calculate the trend (Figure 4), we find that 19.8% of the total number of cloudy days correspond to the year 2007, whereas in 2014 and 2015, this proportion does not exceed 5%. Despite these differences, it is important to highlight that the MODIS products track the long-term trend of the in situ data in the study area, as found for the MOD10A1 (C5) product by Calleja et al. [12] 3.2. Correlation between MOD10A1, MYD10A1 and MCD43 (BSA and WSA) with In-Situ Data In this section, the MODIS albedo values are compared with the in situ albedo values, both for all-sky and clear-sky conditions, with all available data and also for the J-F-M data, after all filters were applied. Although many authors have described the correlation between MODIS albedo data and in situ data in the Greenland ice sheet, the relationship between both types of data in our study area in terms of correlation has not been described to date. However, the MOD10A1 product has been shown to track the trend of in situ data. Figures 5 and 6 show the correlations between the different MODIS products and the in situ data for all-sky and clear-sky conditions. Tables 3 and 4 show the statistics of the differences between MOD10A1, MYD10A1, and MCD43 (BSA and WSA) versus the in situ data in both periods, for all sky (Table 3) and for clear sky ( Table 4).
The results of this work show that the MODIS product that best reflects the behavior of the in situ data for the study area is MOD10A1. High values of the correlation coefficient (r) have also been found between MOD10A1 and the Greenland in situ data obtained by Box et al. [20], for the summer months in the range of 0.92 to 0.97; these values were higher than those obtained in our work for all sky (0.5) and for clear sky (0.7). The remainder of the MODIS products analyzed in our work show greater discrepancies with the automatic weather station (AWS) data. As mentioned in Section 2.1, the study area is characterized by abundant cloud cover. It is known that the physical properties of clouds, e.g., water content, are factors that can also influence cloud albedo [68]. In these cases, when the MODIS cloud mask fails, the products could be assuming that cloud albedo values are snow albedo. As an example, Figure 7 shows an abundance of clouds over Livingston Island and its surroundings. These images correspond to dates when the MODIS cloud mask failed and MODIS albedo values were given. This would explain in many cases the low values mentioned above. In addition, on clear days, MODIS sometimes underestimates the albedo, which could be due to the fact that the satellite-measured clear-sky snow albedo is generally lower than the in situ measured clear-sky snow albedo [46]. Our data show an RMSE value for MOD10A1 clear sky in the summer months that is slightly higher (0.046) than the average obtained by Box et al. [20] for June, July, and August (0.041) although for all clear-sky data we obtained a similar value of 0.042. In spite of this, the bias of MOD10A1-in situ data is low, between 0.001 (for all sky, all dates) and −0.001 and −0.005 for clear sky, for all dates and for J-F-M, respectively. For all-sky conditions, MYD10A1 shows a value of r = 0.4, which shows a poor agreement between this product and the in situ data. It should be noted that MODIS Aqua had problems on band 6, which were corrected for in C6 [35]. However, the results are worse than those obtained with MOD10A1.        Table 3.  For clear-sky conditions, most MODIS products improve the correlation with the in situ data, specifically MOD10A1, which reaches a value of r = 0.7, slightly lower than that indicated by Stroeve et al. [25] with the data from five stations of the Greenland station network (0.79 for MOD10A1). However, there are no major differences with the results obtained in our study for all sky. In addition, low biases are observed in the values of all MODIS products, both for clear days and for all-sky conditions. This reinforces the idea that, at least for our study area, it is possible to use the MODIS albedo for all-sky conditions, as already tested in Calleja et al. [12], which would allow a larger number of data to be available without large differences with the clear-sky data. In addition, although r values may sometimes be worse than expected, as indicated in the previous section, MODIS products follow the in situ data trend. As discussed in the previous section, the cloudiness in the study area is a major problem for the availability of satellite data on clear days, so using all data is a significant advantage.
Regarding MCD43, close values of r were obtained in the summer months for all-sky conditions and for clear sky (0.5-0.6, respectively). The RMSE varied between 0.07 and 0.05, for all sky and clear sky, respectively. These values are higher than those obtained by Wang et al. [74], who described that MCD43 estimates the snow albedo with an average RMSE of 0.04 in Greenland. Our RMSE values for clear sky are similar to those obtained by Tedesco et al. [22] with GLASS surface albedo product data, derived from a combination of data collected by the AVHRR and MODIS, (0.048, June; 0.0455, July; 0.05, August). As can be seen in Table 4, the RMSE values improved on clear-sky days, between 0.053-0.052 (BSA, for all clear-sky data and for J-F-M, respectively) and 0.051 (WSA, for all dates and for J-F-M). However, for all-sky and clear-sky conditions, our RMSE is lower than that obtained by Stroeve et al. [50] for most of their stations, at one of which it reached an RMSE value of 0.129. It must be taken into account that all the data we obtained for the study area correspond to the backup algorithm. This lack of maximum quality data is probably due to the low percentage of total inversion data in MCD43 C6 at latitudes between 50 and 70 • S, as described Wang et al. [31], which provide a percentage of total inversion of 5.5. In addition, several authors [74,75] have recognized that there are still uncertainties in snow albedo recovery, and that it remains an objective to model snow BRDF with very high accuracy from satellite data due to the difficulties of MODIS to detect clouds and factors such as atmospheric correction. Furthermore, although the Ross Thick-Li Sparse Reciprocal (RTLSR) model is able to describe the reflectance anisotropy of a large variety of global land covers [74], the underestimation of albedo compared to in situ albedo measurements may be caused by the operational MODIS BRDF/Albedo algorithm in the MCD43 product, which may not be appropriate for modeling snow BRDFs, as some authors have indicated [76][77][78]. This underestimation of snow albedo has also been described for ephemeral snow with the BRDF/standard albedo product from MODIS (C5) [75].
Regarding the comparison of in situ data with MODIS WSA and BSA, it is worth noting that the correction introduced by calculating the blue-sky albedo with Equation (3) would be a minor. We note that the difference between MODIS BSA and MODIS WSA products is small and increases with increasing SZA. Effectively, MODIS BSA and WSA attain the same value on 24.3% of the total number of days. The relative error between BSA and WSA (e calculated with Equation (5)) does not exceed 0.01 (1%) on 41% of the total number of days, and on 96.5% of the days it is less than or equal to 3%. We calculated e for days with SZA < 60 • and days with SZA > 60 • separately. The reason for this partitioning was explained above. Although the mean value of e for all the days is e = 0.016 (1.6%), the mean value for days with SZA < 60 • is e(SZA < 60 • ) = 0.014 (1.4%), and for the days with SZA > 60 • is e(SZA > 60 • ) = 0.022 (2.2%). The maximum value is e max = 0.055 (5.5%), attained on April 9 2013, a value close to the theoretical predictions using Equation (4). In addition, a simple calculation demonstrates that the relative difference between MODIS blue-sky albedo (BHR), and MODIS BSA (ρ dir ) and MODIS WSA (ρ di f f ), is always smaller than e. Effectively, it is easy to demonstrate from Equation (3) that, for a given value of d, we have: It is obvious from Equations (9) and (10) that e (BHR, ρ diff ) < e, and e (BHR, ]ρ dir ) < e for any value of d. According to the values given above, the mean relative error when taking either MODIS BSA or MODIS WSA for MODIS blue-sky albedo is below 1.6% for all the days, below 1.4% for SZA < 60 • , and below 2.2% for SZA > 60 • . We conclude that the values of BSA and WSA are very close to each other. When BSA and WSA are nearly identical they approach the blue-sky albedo, and can be compared with the albedo measured in situ [50].
In general, for all MODIS albedo products, the correlation improves in the years in which the mass balance in Hurd Glacier was negative, from 2002 to 2007 according to Sancho et al. [71] (for our study period the years 2006 and 2007 were considered). Values between r = 0.6 (MOD10A1, MYD10A1, and BSA) and r = 0.7 (WSA) for all 2006-2007 data, under all-sky conditions, and, except for MYD10A1 (r = 0.5), up to 0.9 for all other MODIS products in clear sky, were obtained. Recent studies have found, when analyzing the relationship between the minimum albedo averaged over glacier (AMAAG) using MODIS data and glacier-wide annual mass balance (Ba), that the agreement is better for negative mass balance years [21]. This is consistent with the best correlations between the MODIS albedo and the in situ data obtained in 2006 and 2007.

Conclusions
This paper shows that albedo products of the MODIS sensor from the C6 data can be used to estimate the albedo for all-sky and clear-sky conditions on Livingston Island, Antarctica. Given the high cloud cover conditions affecting latitudes poleward of 60 • S, it is necessary to evaluate data from satellites/sensors with high temporal resolution, and, consequently, this evaluation can be of interest to improve the accuracy of the snow BRDF/albedo modeling.
It was found that all MODIS albedo products describe an increasing trend in albedo in the study period (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015), consistent with the results of previous investigations. This also corroborates the results obtained with the in situ data, although when there is a higher percentage of cloudy days (19.8% in 2007, and 14% in 2009 and 2012), MODIS albedo values are, generally, lower than in situ albedo values.
The best correlation of the MODIS albedo with the in situ albedo was obtained with the MOD10A1 product for clear days. However, few differences were found between the results obtained for all-sky conditions and those obtained for clear days. Although the MYD10A1 albedo and that provided by the MCD43 product (BSA and WSA) show a worse agreement with the in situ data, they follow the albedo trend measured in the AWS. Furthermore, it should be noted that the MCD43 product only has backup algorithm values in the study area. In summary, we found that cloud cover causes a greater dispersion in MODIS data compared to in situ data, in addition to an underestimation of albedo. Future improvements in snow albedo estimation from satellites should pay particular attention to the distinction between snow and thin clouds, and to the detection of snow edges. Improvements can be made to the cloud mask algorithms and data filtering. In future research, we intend to describe the albedo behavior at other sites in the archipelago and to obtain an algorithm that will allow us to relate MODIS data to in situ data incorporating other variables, such as temperature.