*3.2. Model Parameters*

Only the results for the black-sky albedos are presented henceforth. For other results, please refer to the Supporting Information. Starting with non-forest land cover types, the regression parameters

for the three broadband albedos (black-sky) at the local solar noon are presented in Table 2. The zero degree albedos (all bands) under snow-covered conditions (*<sup>α</sup>*0,*sc*,*<sup>i</sup>*) were generally highest for the "Open" and "Peat bog" land cover types.

**Table 2.** Black-sky albedo model parameters for the non-forested land cover types. "CRO" = croplands; "PAS" = pasture; "O-v" = Open, vegetated; "O-pv" = Open, partly vegetated; "O-sp" = Open, sparsely vegetated; "PB-f" = Peat bog, forested; "PB-nf" = Peat bog, non-forested; "O-nv" = Open, non-vegetated; "U&T" = Urban & transport; "FW" = freshwater; "FOR" = forest. "*α*0,*sc*" = local noon albedo under snow-covered conditions when air temperature (T) equals 0 ◦C; "*α*0,*s f* " = local noon albedo under snow-free conditions when air temperature (T) equals 0 ◦C; "*ρsc*" = air temperature sensitivity parameter for snow-covered conditions; "*ρs f* " = air temperature sensitivity parameter for snow-free conditions.


For shortwave (SW), zero degree albedos under snow-free conditions (*<sup>α</sup>*0,*s f* ,*i*) were lowest for the two non-vegetated categories ("U&T" & "FW"). Snow-free albedos for the near-infrared (NIR) broad band tended to increase with increasing vegetation cover. For instance, NIR *<sup>α</sup>*0,*s f* ,*i* was higher for forested peat bogs ("PB-v") than for non-forested peat bogs ("PB-nf"), and higher for vegetated open ("O-v") than for partly or sparsely-vegetated open land cover types ("O-pv", "O-sv"). The influence of vegetation on *<sup>α</sup>*0,*s f* ,*i* was less clear for the visible (VIS) broad band. For non-vegetated open areas ("O-nv") which typically reside at the highest altitudes, *<sup>α</sup>*0,*s f* ,*i* was higher than that of fully vegetated open areas ("O-v") and of vegetated peat bogs ("PB-f").

For all land cover types (endmembers) and for all broad band albedos, the parameter relating the endmember albedo under snow-covered conditions to the monthly air temperature (i.e., *ρsc*,*<sup>i</sup>*) was negative, which is consistent with numerous observations elsewhere [47,50,51,82,83]. For the croplands and pastures occupying lowland regions, *ρs f* ,*i* for the SW albedo was positive and appeared to be driven by the positive *ρs f* ,*i* for the NIR albedo. For "Open" and "Peat bog" cover types, *ρs f* ,*i* for SW was negative and appeared to be driven by a negative *ρs f* ,*i* in the VIS band.

For forested endmembers, the parameters for the models that were fit with the stand volume as the structural predictor (*xi* in Equations (3) and (4)) are presented in Table 3. Under snow-covered conditions, *α*0 was highest for VIS and lowest for NIR broad bands while the opposite was true for snow-free conditions. The magnitudes of the zero structure forest temperature sensitivity parameter *ρ*0 follow the same pattern. Under snow-covered conditions, the difference in the albedo between a zero structure and a fully developed forest when air temperature is zero (i.e., *βsc*) was largest in the VIS band and smallest in the NIR band, whereas the opposite was true for snow-free conditions (*βs f*). Under snow-covered conditions, the difference in the albedo between a zero structure and a fully developed forest decreased with decreasing air temperature, which provided positive values for *ρsc* for all forest endmembers and albedo bands. The lack of foliage during the months with snow at the

surface likely explains why the temperature sensitivity parameter *ρsc* was larger (in magnitude) for the deciduous endmember ("DBF") than for pine and spruce.

**Table 3.** Black-sky albedo model parameters fit for forests with stand *volume* as the structural predictor. "DBF" = Deciduous broadleaf forest (*Betula* spp.); "*α*0,*sc*" = local noon albedo of forests with zero volume under snow-covered conditions when air temperature (*T*) equals 0 ◦C; "*βsc*" = difference between *<sup>α</sup>*0,*sc* and the asymptotic albedo when *T* equals 0 ◦C; "*α*0,*s f* " = albedo (local noon) of forests with zero volume under snow-free conditions when *T* equals 0 ◦C; "*βs f* " = difference between *<sup>α</sup>*0,*s f* and the asymptotic albedo when *T* equals 0 ◦C; "*λsc*" = an extinction coefficient for snow-covered conditions; "*λs f* " = an extinction coefficient for snow-free conditions; "*ρsc*" = air temperature sensitivity parameter for snow-covered conditions; "*ρs f* " = air temperature sensitivity parameter for snow-free conditions; "*ρ*0,*sc*" = air temperature sensitivity parameter for snow-covered conditions for zero volume forests; "*ρ*0,*s f* " = air temperature sensitivity parameter for snow-free conditions for zero volume forests.


As for the snow-free temperature sensitivity parameter *ρs f* , the values in all bands were negative for the spruce and pine endmembers. However, we found positive *ρs f* values for DBF in the VIS band. A likely explanation is that the leaf area tends to increase with increasing temperature, and for DBF, the VIS albedo of *Betula* spp. bark and branches (especially in the green (560 nm) and red (660 nm) bands [84]) is higher than that for foliage [85,86]. The positive *ρs f* in the VIS band appeared to outweigh the negative *ρs f* in the NIR band, resulting in a positive *ρs f* for the entire SW broadband albedo (Table 3).

The shape parameters *λsc* and *λs f* in each broad band were similar in sign and magnitude for all the endmembers and were largest in the VIS band. The negative values sugges<sup>t</sup> that the albedos decreased with increasing aboveground volume (or biomass), and that the total surface albedo was driven by the canopy masking of the ground surface and understory. This result can be more fully appreciated when looking at Figure 4.

#### *3.3. Model Behavior in Forests*

For forests, the model behavior under both snow-covered and snow-free conditions is only presented for the volume models (Figure 4) although the models behaved similarly for biomass (Supporting Information Figures S3 and S4). To illustrate this behavior, we fixed *SC* at two extremes —0.75 (snow-covered) and 0 (snow-free)—and two temperature extremes at these two *SC* extremes. The shaded area between the solid and dashed curves in Figure 4 illustrates the effect of the temperature sensitivity parameter.

The albedo in all broad bands increased with decreasing temperatures during the snow season. The factors that were likely contributing to the differences between the −12◦ and 2◦ curves shown in Figure 4A were the amounts of snow intercepted and held by forest canopies and the physical

properties of snow itself. For instance, when the monthly *SC* is 0.75 and monthly *T* is −12 ◦C, the monthly albedos of a young or newly harvested stand (i.e., when volume = 0) can be as high as 0.86, 0.67 and 0.54 for the VIS, SW and NIR bands, respectively. These values reduce as the forests age and the stand volume (or aboveground biomass) increases. For the pine and spruce endmembers, Figure 4A suggests that the albedo varies only slightly above ~150 m<sup>3</sup> ha−1. However, the asymptotic albedo is not reached within the plotted range for DBF (i.e., 450 m<sup>3</sup> ha−1).

**Figure 4.** Black-sky albedo model behavior for forest endmembers using mean stand *volume* as the structural predictor: (**A**) with maximum snow cover and (**B**) with zero snow cover. It is important to note the differences in y-axes scaling. "DBF" = deciduous broadleaf forest.

Turning our attention to the forest endmember model behavior under snow-free conditions (Figure 4B), the albedos were highest in the NIR band and lowest in the VIS band. In all broad bands, the albedos were generally highest in DBF and lowest in spruce. The albedo variation with temperature is represented by the shaded areas and is largest for the NIR band. For the spruce and pine endmembers, the highest albedos for any broad band corresponded to the warmest periods. However, the VIS albedo (Figure 4B, solid curve) was highest when the air temperatures were lowest for DBF (i.e., during the shoulder seasons). This may be explained by the lack of foliage that exposed light-colored stems, which are characteristic of the birch species (*Betula* spp.) in our study region. This was in contrast to the relationship between the temperature and NIR albedo where, similar to pine and spruce, the NIR albedos for DBF were highest during the warmest periods (Figure 4B, top panel, dashed green curve). This contrast results in a much narrower range of SW albedo for DBF under snow-free conditions (Figure 4B, middle panel, green shaded area), particularly at high stand volumes. The range of the albedo variation with temperature is larger for all tree species for the white-sky albedos (Supporting Information Figures S2 and S4).

#### *3.4. Model Benchmarking and Validation*

Given their slightly higher accuracy, only the prediction error for the models fit at the effective spatial resolution is presented henceforth. Starting at the pixel level, Figure 5 illustrates the geospatial distribution of the seasonal error (SW broadband, black-sky) within the validation region. The largest errors in all seasons were mostly confined to the higher elevation regions of the north and west. The largest errors were found in winter (DJF) in these regions—regions with monthly *T* and *SC* values at the edge of or exceeding the range found in the model training region. In general, the largest positive errors (red values, Figure 5) in winter were found over the largest inland waterbodies ("FW"). Although this error was reduced, the positive error seen over larger freshwater bodies was also evident in spring (MAM) and autumn (SON). On average, the mean *SC* over these larger freshwater bodies during the colder seasons in 2006–2010 was found to be lower than for the smaller freshwater bodies, which resulted in overestimates of the surface albedo when combined with a low temperature sensitivity parameter (*ρsc*, Table 2). For all seasons, the larger negative errors (blue values) were typically found for pixels with larger proportions of the two open area types "O-nv" and "O-sv", which were mostly concentrated at the higher elevation regions of the north and west (Figure 5, third column of sub-panels).

**Figure 5.** Seasonal prediction error for the shortwave broadband surface albedo (black-sky, at local solar noon) in the validation region. Black values in the error subpanels denote pixels with zero high-quality MCD43A3 or MOD10A1 retrievals during the five-year sample period. "DJF" = December-January-February; "MAM" = March–April–May; "JJA" = June-July-August"; and "SON" = September-October-November.

Moving on to forests, the seasonal prediction errors in the validation domain for the volume-based models are reported in Figure 6 for all bands. The largest errors were found in winter ("DJF"; Figure 6) for DBF where the variations in structure not explained by stand total volume were larger than in snow-free seasons. In winter, the DBF model had a high prediction error, with a median of ~0.05 for all bands. The absolute error for 50% of the predictions (i.e., the interquartile range) for all bands fell within ~0.07–0.17. For other forest types, the median and interquartile errors were smaller. A median positive error of ~0.025 (all bands) was found for spruce. For pine, the median errors were negative for all bands although this error was lower for the NIR band. Combining the parameters for pine and spruce resulted in the lowest median and interquartile error ranges for mixed-conifer forests ("ENF"). Although the median errors were equally low for mixed forests ("MF"), the error interquartile ranges were approximately double that of ENF. For SW, the mean of the median errors for all forest types was 0.01, or ~3% of the mean SW albedo of forests during DJF.

**Figure 6.** Seasonal error in black-sky albedos (local noon) for pixels with greater than 95% forested area (effective resolution) of one forest type. Predictions are based on the forest models fit with stand volume. "Spruce" = spruce forest (n = 20,260); "Pine" = pine forest (n = 12,167); "ENF" = Evergreen needleleaf forest (n = 100); "MF" = Mixed forest (n = 148); "DBF" = Deciduous broadleaf forest (n = 4175); "SW" = shortwave broadband albedo (250–5000 nm); "NIR" = near infrared broadband albedo (700–5000 nm); and "VIS" = visible broadband albedo (250–700 nm). Horizontal lines represent the medians, boxes represent the interquartile ranges and dashed whiskers represent the extent of the upper and lower quartiles.

Turning our attention to spring (Figure 6; "MAM"), median prediction errors in all forests were found to be similar to those in DJF. However, a major difference was that errors in MAM were much more tightly distributed around the median values. In other words, the error interquartile ranges in MAM were approximately 25–40% of those found for DJF. The improved accuracy in MAM was unsurprising given that a larger share of the high quality MCD43A retrievals representing snow-covered conditions stemmed from MAM, thus influencing the snow-covered model parameters more heavily. Similar to DJF, the largest errors in MAM were found in DBF and MF. For SW, the

mean of the median errors for all forest types was 0.01, or 4.5% of the mean SW albedo of forests during MAM.

The lowest errors were found during summer ("JJA"; Figure 6). Whereas median error and error interquartile ranges for the three broad bands were similar in magnitude for winter and spring, the median and interquartile errors in the NIR band in JJA were notably larger than that for the VIS band. For the SW band, the mean of the median error for all forest types was 0.0025, or ~2% of the mean SW albedo of forests during JJA.

As for JJA, the error interquartile ranges for the NIR band were larger than for the VIS band during autumn ("SON"; Figure 5). The spread in error in SON was second largest after DJF although median errors were similar. As for DJF and MAM, the spread in errors (interquartile ranges) was largest for DBF.

For all forested pixels included in the validation exercise, predictions (SW black-sky only) were also compared to predictions from the empirical models of Bright et al. [27] which were based on forest age and *T* (Figure 7).

**Figure 7.** Seasonal mean error in predicted albedo in forests (SW black-sky) between the *Volume*-based models and the *Age-*based models of Bright et al. [27]: ( **A**) December-January-February; (**B**) March-April-May; ( **C**) June-July-August; and ( **D**) September-October-November. Horizontal lines represent the medians, boxes represent the interquartile ranges and dashed whiskers represent the extent of the upper and lower quartiles.

Starting in winter ("DJF"; Figure 7A), compared to the *Ag*e-based models the *Volume*-based models presented in this work appeared to slightly improve the DJF accuracy in forests judging by the median errors, with the exception of pine. For pine, the median error using the *Volume* model was similar to that of the *Age* model. The spread in errors for the *Volume* models were similar to the *Age* models, although the error interquartile ranges appear to have been slightly reduced for pine, ENF and MF with the *Volume* models.

For spring ("MAM"; Figure 7B), the median errors for ENF, MF and DBF using the *Volume* models were notably reduced compared to the *Age* models. The error interquartile ranges were reduced for all forest types although for spruce and pine, the median errors were slightly higher (in absolute terms).

In summer ("JJA"; Figure 7C), the median prediction errors were noticeably reduced in most forest types compared to the *Age* models. The exception is DBF where the median error using the *Age* model was slightly lower than that of the *Volume* model.

The most notable improvements over the *Age*-based models were found in the autumn months ("SON"; Figure 7D), which demonstrates that while monthly mean *T* may be a good proxy for snow during winter and spring, it suffers as a proxy for snow during autumn. Relative to the *Age* models, the application of the *Volume* models led to large reductions in the median errors in all forest types with the exception of DBF, where the median errors were similar.

Shifting our attention to the non-forest endmembers and the limiting results presented henceforth of the full SW broad band, spreads in model errors were largest in DJF as expected (Figure 8, upper left panel). Median prediction errors were under 0.05 for all land cover types, except for "O-sv", "PB-f" and "O-nv". Median errors for "O-sv" and "O-nv" were negative for each season. Median error for "PB-f" was positive for all seasons although we note that the number of MCD43A3 retrievals containing "PB-f" homogeneity to ≥95% was limited to just three.

**Figure 8.** Seasonal error in shortwave black-sky albedo for non-forested land cover types (endmembers) for pixels with greater than 95% area (effective resolution) of one type (**Upper left**) December-January-February; (**Upper right**) March-April-May; (**Lower left**) June-July-August; and (**Lower right**) September-October-November. "CRO" = croplands (n = 3504); "PAS" = pasture (n = 11); "O-v" = Open, vegetated (n = 21,930); "O-pv" = Open, partly vegetated (n = 11,966 ); "O-sv" = Open, sparsely vegetated (n = 21,330); "PB-f" = Peat bog, forested (n = 3); "PB-nf" = Peat bog, non-forested (n = 1561); "O-nv" = Open, non-vegetated (n = 19,900); "U&T" = Urban & transport (n = 1498); and "FW" = freshwater (n = 17,573). Horizontal lines represent the medians, boxes represent the interquartile ranges and dashed whiskers represent the extent of the upper and lower quartiles.

In order to more rigorously assess whether these error patterns were systematic, we relaxed the homogeneity requirement described in Section 2.9 and recomputed the error statistics for all pixels using the sub-MODIS pixel modes from AR5/SR16 to define the majority land cover type. Figure 9 contains the results after normalizing the seasonal mean prediction error to the MCD43A3 retrievals, which reinforces the above-mentioned results that error patterns for "PB-f", "O-sv" and "O-nv" were indeed systematic.

**Figure 9.** Normalized error (SW black-sky) by season and land cover (endmember) type; (**Upper left**) December-January-February; (**Upper right**) March-April-May; (**Lower left**) June-July-August; and (**Lower right**) September-October-November Pixels were allocated to individual land cover types according to the largest relative land cover fraction within the MCD43A3 v6 *effective* spatial resolution. Whiskers denote 2σ sigma confidence intervals, boxes denote interquartile ranges, and red horizontal lines denote medians. The gray shaded area represents the accepted error range of ±0.1 (±10%).

Figure 9 also shows that the range in errors for freshwater ("FW") relative to the retrieved values is the largest among all land cover types, particularly in autumn (Figure 9 SON and JJA, whiskers). Given an acceptable median error threshold of ≤10%, Figure 9 shows that all models except "PB-f", "O-sv," and "O-nv" are accurate in spring (MAM) and summer (JJA). In winter, median normalized errors of all models except "O-nv" and "PB-f" meet this accuracy threshold. For autumn, median normalized errors of all models except "PB-f", "PB-nf," and "FW" meet this threshold. Additionally, the large spread in error for "Birch" (Figure 6) causes the median normalized error for forests as a whole ("FOR" in Figure 9) to slightly exceed the 10% accuracy threshold.
