Guangdong Key Laboratory for Urbanization and Geo-simulation Sun Yat-sen University, Guangzhou, China. University of California, Irvine, USA

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1 Auxiliary Material Submission for Paper: Reply to Schaaf, Wang and Strahler: Commentary on Wang and Zender MODIS snow albedo bias at high solar zenith angles relative to theory and to in situ observations in Greenland Introduction: 1,2 Xianwei Wang and 2 Charles S. Zender 1 School of Geography and Planning Guangdong Key Laboratory for Urbanization and Geo-simulation Sun Yat-sen University, Guangzhou, China 2 Department of Earth System Science University of California, Irvine, USA We have analyzed the 500m MODIS albedo product (MCD43A3) and its quality flag (MCD43A2), and the 0.05 product (MCD43C3) in 2005 for examples. These data have been downloaded from the NASA's Land Processes Distributed Active Archive Center (LP DAAC) at: Four MCD43A product tiles (h15v02, h16v02, h16v01, h17v01) have been downloaded to cover the entire Greenland. The MODIS Reprojection Tool (MRT) is used to mosaic the four tiles into one image, and then to resample the sinusoidal to Geographic coordinate, and to spatially subset to cover the almost entire Greenland, 60 N-80 N and 60 W-20 W. The 500 m BRDF albedo quality flag (BRDF_Albedo_Quality) in MCD43A2 only has two valid values, Q=0 processed, good quality (or full BRDF inversions), and Q=1 processed, magnitude BRDF inversions. There is no data labeled as Q=2, and 3, except for Q= 4, the fill value for the 500 m product. The quality flag for the aggregated 0.05 product in MCD43C3 has five values. Q=0 best quality, 75% or more with best full inversions; Q=1 good quality, 75% or more with full inversions; Q= 2 mixed, 75% or less full inversions and 25% or less fill values; Q=3 all magnitude inversions or 50% or less fill values; Q=4, over 50% fill value. We use these quality flag values to separate the MODIS shortwave broadband snow albedo into different classes. All statistic analysis is constrained by these quality flags. The results are plotted in the following 10 figures. S.Figure 1 compares the snow albedo values from the 500 m product (MCD43A3) and from the 0.05 product (MCD43C3) within one 0.05 grid at Summit in Greenland. There are 16 MCD43A3 500m grids within one 0.05 grid at Summit. Snow albedo values from the 500 m and the 0.05 data are virtually identical, and both decrease with solar zenith angle (SZA) increase when SZA is larger than ~55. This indicates that spatial representative from the 500 m and the 0.05 data and from the BSW and WSA is near identical. S.Figures 2 and 3 display the mean MODIS snow albedo from the 0.05 product (MCD43C3) and 500 m product (MCD43A3) respectively for each retrieval quality categories within each solar zenith angle (SZA) in the central Greenland from 60 N to 80 N and from 40 W to 50 W on days in Only pixels whose albedo value is larger than 0.5 and snow cover fraction (SCF) is 100% (for snow) are counted. According to the 0.05 product (MCD43C3) in 1

2 S.Figure 2, it clearly shows that the reduced albedo trend at high SZA is much less pronounced for Q=0 data than for Q>0 data; for Q=0 the decline trend only appears for SZA > ~70, whereas for Q>0 the trend appears "earlier", i.e., albedos begin decreasing after SZA >~60. The White Sky Albedo (WSA) decreases more quickly with SZA (for large SZA) than does the Black Sky Albedo (BSA). What is the sensitivity of our results from the 0.05 product (MCD43C3) to the resolution and quality of the input data used, i.e., the 500 m product (MCD43A3)? According to S.Figure 3, the retrieved albedo from the 500 m product decreases with SZA for SZA > ~60. This is the same qualitative behavior seen in the 0.05 data in S.Figure 2. Quantitatively, the 500 m albedo has a similar pattern with that of the 0.05 product and decreases faster with SZA than the 0.05 data. Second, the retrieved 500m albedo shows only a small difference with quality levels (Q=0, 1, or all) for different SZAs. S.Figure 4 shows pixel ratio (pixel ratio = pixel_count_qx/pixel_count_all_q, x=0,1,2,3,4) of the 0.05 product (MCD43C3) and 500 m product (MCD43A3) for each retrieval quality flag within each solar zenith angle (SZA) in the central Greenland from 60 N to 80 N and from 40 W to 50 W on days in Only pixels whose albedo value is larger than 0.5 and snow cover fraction (SCF) is 100% are counted. The pixel ratio (pixel count for Q=0 divided by the total pixels for all Q levels) for high quality flag values (Q=0) at large SZAs (65-80 ) from 500 m data demonstrate a increase trend while it is a decrease trend in the 0.05 data. The highquality retrieval (Q=0) snow albedo data are ~35% of all retrievals in a year in Greenland and have very sparse coverage of northern Greenland. S.Figures 5-8 shows the zonal mean white-sky and black-sky shortwave snow albedo for the high-quality retrievals of Q=0 and low-quality retrievals of Q>0 from the 0.05 product (MCD43C3) and 500 m product (MCD43A3) respectively within each latitude zone (e.g., N62 to N77 ) from 50 W to 40 W in central Greenland. These figures are complementary to Figure 8 in Wang and Zender (2010a), which does not separate the high-quality retrievals from the lowquality retrievals that have been complained by Schaaf et al. (2011). These figures verify that the decrease trend of MODIS snow albedo with SZAs is dominated by the low-quality retrievals when SZAs are larger than ~55 and by all-quality retrievals when SZAs are larger than ~70. The results from 500m MODIS snow albedo data (MCD43A3) confirms the results derived from the 0.05 product (MCD43C3). S.Figures 9 and 10 shows examples of the spatial distributions of the high/low-quality retrievals and corresponding snow albedo values from the 0.05 product (MCD43C3) and 500 m product (MCD43A3) on day 73, 2005 in Greenland, respectively. The SZA at 65 N and 75 N are near 65 and 75 on day 73, respectively. These figures illustrate that the high-quality retrievals concentrates in the southern Greenland, while low-quality retrievals are in the northern Greenland. The low-quality retrievals display unrealistic snow albedo values and dominate significant fractions of Greenland. The dearth of the high-quality retrievals requires the community to use the low-quality retrieval data in order to obtain a full spatial and temporal coverage (Oleson et al., 2003; Zhou et al., 2003; Wang et al., 2004), but such low-quality retrieval data can not be directly used unless similar adjustments as suggested by Wang and Zender (2010b) are implemented. 2

3 S.Figure 1. Comparison of MCD43A3 (500m) and MCD43C3 (0.05 ) albedo values within one 0.05 grid at Summit in Greenland. There are 16 MCD43A3 500m grids within one 0.05 grid at Summit. 3

4 S.Figure 2. Mean MODIS snow albedo (MCD43C3, A for White-sky albedo, B for Black-sky albedo) for each retrieval quality categories within each solar zenith angle (SZA) in the central Greenland from 60 N to 80 N and from 40 W to 50 W on days in Only pixels whose albedo value is larger than 0.5 and snow cover fraction (SCF) is 100% (for snow) are counted. 4

5 S.Figure 3. Mean MODIS snow albedo (MCD43A3, A for White-sky albedo, B for Black-sky albedo) for each retrieval quality categories within each solar zenith angle (SZA) in the central Greenland from 60 N to 80 N and from 40 W to 50 W on days in

6 S.Figure 4. MODIS albedo (A. MCD43C3 (0.05 ), B. MCD43A3 (500m) pixel ratio (pixel ratio = pixel_count_qx/pixel_count_all_q, x=0,1,2,3,4) for each retrieval quality flag within each solar zenith angle (SZA) in the central Greenland from 60 N to 80 N and from 40 W to 50 W on days in Only pixels whose albedo value is larger than 0.5 and snow cover fraction (SCF) is 100% are counted. 6

7 S.Figure 5. Zonal mean MCD43C3 (0.05 ) white-sky shortwave snow albedo within each latitude zone (e.g., N62 to N77 ) from 50 W to 40 W in central Greenland. A is for the best retrieval that Q=0, and B is for Q=1, 2, 3 and 4 for magnitude inversions. F 7

8 S.Figure 6. Zonal mean MCD43C3 (0.05 ) black-sky shortwave snow albedo within each latitude zone (e.g., N62 to N77 ) from 50 W to 40 W in central Greenland. A is for the best retrieval that Q=0, and B is for Q=1, 2, 3 and 4 for magnitude inversions. 8

9 S.Figure 7. Zonal mean MCD43A3 (500 m) white-sky shortwave snow albedo within each latitude zone (e.g., N62 to N77 ) from 50 W to 40 W in central Greenland. A is for the best retrieval that Q=0, and B is for Q=1 for magnitude inversions. 9

10 S.Figure 8. Zonal mean MCD43A3 (500 m) black-sky shortwave snow albedo within each latitude zone (e.g., N62 to N77 ) from 50 W to 40 W in central Greenland. A is for the best retrieval that Q=0, and B is for Q=1 for magnitude inversions. 10

11 S.Figure 9. MCD43C3 (0.05 ) black-sky (left) and white-sky (right) albedo map for those quality flags of Q=0 (top) and for all Q retrievals (bottom) Greenland on day 73, The SZA at 65 N and 75 N are near 65 and 75 on day 73, respectively. 11

12 S.Figure 10. MCD43A3 (500m) black-sky (left) and white-sky (right) albedo map for those quality flags of Q=0 (top) and for all Q retrievals (bottom) Greenland on day 73, The SZA at 65 N and 75 N are near 65 and 75 on day 73, respectively. 12