*3.3. Residuals Analysis*

The main purpose of validation is to evaluate and improve the model accuracy. The residual between VSIA and PROMICE albedo measurements were analyzed with the related factors. First, the seasonal change of albedo values and the bias trend were observed. Second, the annual trend of the most important environmental factor for snow/ice albedo (SZA) was analyzed with the albedo time series and residuals. Finally, the influence of another important factor for in situ validation—ground heterogeneity—was also considered.

#### 3.3.1. Temporal Continuity and Variability of Albedo

Figure 6 demonstrates the annual variation curves of the VSIA and PROMICE albedo. It is shown that the VSIA albedo and PROMICE albedo time series agree well with a cross-correlation coefficient of 0.9554, illustrating a significantly strong correlation.

The surface albedo of the ablation area changes with the coverage fractions of snow, bare ice, and dark impurity-rich surfaces. Accordingly, the corresponding difference fluctuates at different seasons along with the ice/snow melting and accumulating cycle. Albedo value fluctuates intensely in winter responding to the snow events. Snowfall will cause a large albedo value and its melting will decrease the surface albedo. When summer approaches, the ice melts first and the pond fraction increases, causing the albedo to drop to its minimum value at the end of July. Then, the freezing of ponds increases the albedo again.

**Figure 6.** Seasonal cycle of clear-sky noon time albedo averaged over all PROMICE stations and the corresponding VSIA. The line is the 6-year average from 2012 to 2017

## 3.3.2. Influence of Heterogeneity

Considering the complex land cover types and the topography variation that surrounds many of the PROMICE stations, the standard error of albedo in the 3 × 3 neighboring pixels was analyzed to assess the effect of the local heterogeneity, as shown in Figure 7.

**Figure 7.** The average standard deviation (STD) of VSIA albedo within 3 × 3 neighboring pixels at each station and the standard deviation of albedo residuals over all match-ups. Each color corresponds to one region.

Here, a range of 3 × 3 VIIRS neighboring pixels is chosen to assess the spatial heterogeneity at satellite level considering the maximum geolocation error of VIIRS M-band SDR data [48]. Figure 7 illustrates the mean standard deviation of albedo within 3 × 3 neighboring pixels and the standard deviation of the residuals between VSIA and PROMICE albedo at the center pixel. It is shown that the albedo heterogeneity is correlated with the spread of the match-up residuals within the same region. This inference is not applicable for cross-region comparison due to the interference from the different albedo magnitudes and distinct land cover compositions. Exceptions include stations in the QAS region and the THU region, which may be due to the limitation of the albedo map used in our analysis. A higher resolution albedo map is preferred to assess the around-site heterogeneity.

#### 3.3.3. Influence of Solar Zenith Angle

Due to the high latitude of the Greenland region, the solar zenith angle corresponding to the observations are distributed from 38◦ to 82◦ and peak around 50◦~55◦, as shown in Figure 8.

The bias between the VIIRS albedo and PROMICE observations exhibit a slight increasing trend with SZA, as shown in Figure 9. SZA determines the fraction of the direct incident radiation and the directional-hemispherical albedo component. It influences the diurnal/seasonal variation of surface albedo. For clear-sky snow/ice albedo, the photons interact with the snow grains over a longer path at larger SZAs, which will result in more interaction with snow surface and higher absorption [49]. At larger SZAs, the retrieval uncertainty of VSIA increases due to the strong anisotropy of the snow/ice surface. Meanwhile, the measurement error of the cosine instrument increases at larger SZAs. They together lead to the larger standard albedo error at larger SZAs.

It is known that SZA at solar noon time is larger in winter than summer. Therefore, a larger bias would be observed in winter.

**Figure 8.** The distribution of SZAs (solar zenith angles) of all match-ups.

**Figure 9.** (**a**) Variation of albedo residuals along with SZA and the monthly mean albedo bias and solar zenith angle (SZA); (**b**) Error bars show the standard deviation of the albedo bias.

#### *3.4. Validation Using GC-NET Match-Ups*

The validation results over GC-NET sites showed a similar estimation accuracy of VSIA albedo to that over PROMICE sites. The absolute value of overall accuracy is 0.025 with a precision of 0.065, as shown in Figure 10. This is acceptable as the precision of GC-NET observations is around 0.05 [38]. The overall root mean square error is 0.07, while the relative RMSE of 0.661 is showing 66% of the unexplained variance. Similar to the PROMICE validation result, VSIA and the GC-NET measured albedo is generally consistent with better agreemen<sup>t</sup> at the ablation zone of lower albedo. Note that some outliers appear at the PetermanELA site, showing larger observations from GC-NET than VIIRS retrievals, that are caused by surface heterogeneity and geometric match uncertainty.

**Figure 10.** Comparison between VSIA and GC-NET clear-sky in situ albedo at 18 automatic weather stations.

The goodness of fit at different sites displays some spatial patterns, as shown in Figure 11. This implies that the validation results are influenced by the elevation, latitude, and land cover types of different sites. The validation results at red-colored sites show that VSIA has an underestimation of albedo compared with GC-NET observations, with a higher RMSE. These sites distribute in the northernmost and southernmost regions and suffer more from surface heterogeneity. At the green-colored sites, VSIA has more accurate estimations and shows lowest bias and RMSE. At the blue-colored sites, VSIA slightly overestimates ground albedo and shows moderate RMSE.

#### *3.5. Evaluation of VSIA Using In Situ Sea-Ice Albedo*

Figure 12 shows the comparison between VSIA and Istomina's measurements [39]. The VSIA values all fell in the range of the ground samples at all the six ice stations. The bias between the two datasets is 0.09. It should be noted that the satellite-derived albedo is instantaneous and averaged spatially; surface measurements are local and averaged temporally. The strong spatial heterogeneity and the albedo variation around the station have introduced large uncertainties to the comparison. Moreover, the in situ measurements were directly averaged without considering the contribution weight of each land cover type due to the lack of auxiliary data. Based on the comparison, we can infer that the VSIA correctly reflects the albedo magnitude of the sea-ice regions covered in the experiment.

The daily mean albedo [40] was collected from one site on different dates. Figure 13 illustrates the time-series plots of VSIA and ground observations. The albedo values generally match with a bias of 0.077. The albedo discrepancy varies along with the sea-ice evolution. (1) The sign of the discrepancy changed at the third match-up because there was a snow event on 20 May so that the spatial distribution of surface albedo changed. (2) The last match-up happens in the sharp snow-melting period. The strong spatial heterogeneity with snow accumulation and melting mainly contributes to the large albedo discrepancy.

**Figure 11.** The distribution of the (**a**) ordinal scaled bias and (**b**) RMSE of all GC-NET sites.

**Figure 12.** Comparison between the VSIA albedo and the in situ measurement in the central Arctic. ROV: Remotely Operated Vehicle. The box plot illustrates the distribution of the in situ sample at each station. The triangles mark the VSIA albedo.

**Figure 13.** Comparison between the VSIA albedo and the in situ measurement near Alaska. The time-series measurements were collected at one station.
